From 9ff1f043c630c4572e6a245baa5c433404b57498 Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Wed, 1 Apr 2026 12:22:42 +0200 Subject: [PATCH 01/11] feat: add control-free optimal control problems support - Add control-free problems documentation and examples - Implement ExponentialGrowth and HarmonicOscillator test problems - Fix error display for zero reference objectives (use absolute error) - Make color thresholds consistent with test tolerances - Add unique IDs to all section headings to avoid anchor conflicts - Fix MD036 linting warnings in documentation - All 84 tests passing successfully BREAKING CHANGE: None (pure addition) Workaround: Uses u(t) penalty term (1e-5*u(t)^2) instead of u(t)==0 constraint Future: Remove u(t) declaration and penalty when native control-free syntax is implemented --- docs/make.jl | 1 + docs/src/api/private.md | 244 +++++++++++++++++++ docs/src/example-control-free.md | 162 ++++++++++++ docs/src/example-double-integrator-energy.md | 9 +- docs/src/example-double-integrator-time.md | 30 +-- docs/src/manual-abstract.md | 46 +++- docs/src/manual-initial-guess.md | 14 ++ docs/src/manual-model.md | 16 +- docs/src/manual-plot.md | 24 +- docs/src/manual-solution.md | 8 +- docs/src/manual-solve-explicit.md | 3 +- test/helpers/print_utils.jl | 41 +++- test/problems/TestProblems.jl | 2 + test/problems/control_free.jl | 94 +++++++ test/suite/solve/test_canonical.jl | 16 +- 15 files changed, 649 insertions(+), 61 deletions(-) create mode 100644 docs/src/api/private.md create mode 100644 docs/src/example-control-free.md create mode 100644 test/problems/control_free.jl diff --git a/docs/make.jl b/docs/make.jl index 5609daab..5492b6d5 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -207,6 +207,7 @@ with_api_reference(src_dir, ext_dir) do api_pages "Basic Examples" => [ "Energy minimisation" => "example-double-integrator-energy.md", "Time mininimisation" => "example-double-integrator-time.md", + "Control-free problems" => "example-control-free.md", ], "Manual" => [ "Define a problem" => "manual-abstract.md", diff --git a/docs/src/api/private.md b/docs/src/api/private.md new file mode 100644 index 00000000..9e4eb360 --- /dev/null +++ b/docs/src/api/private.md @@ -0,0 +1,244 @@ +```@meta +EditURL = nothing +``` + +# Private API + +This page lists **non-exported** (internal) symbols of `OptimalControl`. + + +--- + +### From `OptimalControl` + + +## `DescriptiveMode` + +```@docs +OptimalControl.DescriptiveMode +``` + + +## `ExplicitMode` + +```@docs +OptimalControl.ExplicitMode +``` + + +## `SolveMode` + +```@docs +OptimalControl.SolveMode +``` + + +## `_DEFAULT_DISPLAY` + +```@docs +OptimalControl._DEFAULT_DISPLAY +``` + + +## `_DEFAULT_INITIAL_GUESS` + +```@docs +OptimalControl._DEFAULT_INITIAL_GUESS +``` + + +## `_INITIAL_GUESS_ALIASES` + +```@docs +OptimalControl._INITIAL_GUESS_ALIASES +``` + + +## `_INITIAL_GUESS_ALIASES_ONLY` + +```@docs +OptimalControl._INITIAL_GUESS_ALIASES_ONLY +``` + + +## `_ansi_color` + +```@docs +OptimalControl._ansi_color +``` + + +## `_ansi_reset` + +```@docs +OptimalControl._ansi_reset +``` + + +## `_build_components_from_routed` + +```@docs +OptimalControl._build_components_from_routed +``` + + +## `_build_or_use_strategy` + +```@docs +OptimalControl._build_or_use_strategy +``` + + +## `_build_partial_description` + +```@docs +OptimalControl._build_partial_description +``` + + +## `_build_partial_tuple` + +```@docs +OptimalControl._build_partial_tuple +``` + + +## `_build_source_tag` + +```@docs +OptimalControl._build_source_tag +``` + + +## `_complete_components` + +```@docs +OptimalControl._complete_components +``` + + +## `_complete_description` + +```@docs +OptimalControl._complete_description +``` + + +## `_descriptive_action_defs` + +```@docs +OptimalControl._descriptive_action_defs +``` + + +## `_descriptive_families` + +```@docs +OptimalControl._descriptive_families +``` + + +## `_determine_parameter_display_strategy` + +```@docs +OptimalControl._determine_parameter_display_strategy +``` + + +## `_explicit_or_descriptive` + +```@docs +OptimalControl._explicit_or_descriptive +``` + + +## `_extract_action_kwarg` + +```@docs +OptimalControl._extract_action_kwarg +``` + + +## `_extract_kwarg` + +```@docs +OptimalControl._extract_kwarg +``` + + +## `_extract_strategy_parameters` + +```@docs +OptimalControl._extract_strategy_parameters +``` + + +## `_has_complete_components` + +```@docs +OptimalControl._has_complete_components +``` + + +## `_print_ansi_styled` + +```@docs +OptimalControl._print_ansi_styled +``` + + +## `_print_component_with_param` + +```@docs +OptimalControl._print_component_with_param +``` + + +## `_route_descriptive_options` + +```@docs +OptimalControl._route_descriptive_options +``` + + +## `_unwrap_option` + +```@docs +OptimalControl._unwrap_option +``` + + +## `display_ocp_configuration` + +```@docs +OptimalControl.display_ocp_configuration +``` + + +## `get_strategy_registry` + +```@docs +OptimalControl.get_strategy_registry +``` + + +## `solve_descriptive` + +```@docs +OptimalControl.solve_descriptive +``` + + +## `solve_explicit` + +```@docs +OptimalControl.solve_explicit +``` + + +## `will_solver_print` + +```@docs +OptimalControl.will_solver_print +``` + diff --git a/docs/src/example-control-free.md b/docs/src/example-control-free.md new file mode 100644 index 00000000..fbd3d057 --- /dev/null +++ b/docs/src/example-control-free.md @@ -0,0 +1,162 @@ +# [Control-free problems: parameter estimation and dynamic optimization](@id example-control-free) + +Control-free problems are optimal control problems without a control variable. They are useful for: + +- **Parameter estimation**: identifying unknown parameters in differential equations from observed data +- **Dynamic optimization**: optimizing constant parameters subject to ODE constraints + +This page demonstrates two simple examples with known analytical solutions. + +!!! compat "Upcoming feature" + + The syntax shown here uses a workaround with a dummy control (`u ∈ R, control` and `u(t) == 0`) because the parser does not yet support omitting the control declaration. These workaround lines are marked with `# TO REMOVE WHEN POSSIBLE` and will be removed once native control-free syntax is implemented. + +First, we import the necessary packages: + +```@example main +using OptimalControl +using NLPModelsIpopt +using Plots +``` + +## Example 1: Exponential growth rate estimation + +Consider a system with exponential growth: + +```math +\dot{x}(t) = p \cdot x(t), \quad x(0) = 2 +``` + +where $p$ is an unknown growth rate parameter. We have observed data following $x_{\text{obs}}(t) = 2 e^{0.5 t}$ and want to estimate $p$ by minimizing the squared error: + +```math +\min_{p} \int_0^{10} (x(t) - x_{\text{obs}}(t))^2 \, dt +``` + +The analytical solution is $p = 0.5$. + +### [Problem definition](@id example-control-free-problem-1) + +```@example main +# observed data (analytical solution) +data(t) = 2.0 * exp(0.5 * t) + +# optimal control problem (parameter estimation) +ocp1 = @def begin + p ∈ R, variable # growth rate to estimate + t ∈ [0, 10], time + x ∈ R, state + u ∈ R, control # TO REMOVE WHEN POSSIBLE + + x(0) == 2.0 + + ẋ(t) == p * x(t) + + ∫((x(t) - data(t))^2 + 1e-5*u(t)^2) → min # fit to observed data # TO REMOVE u(t) when possible +end +nothing # hide +``` + +### [Solution](@id example-control-free-solution-1) + +```@example main +sol1 = solve(ocp1; display=false) +println("Estimated growth rate: p = ", variable(sol1)) +println("Objective value: ", objective(sol1)) +println("Expected: p = 0.5, objective ≈ 0.0") +nothing # hide +``` + +```@example main +plot(sol1; size=(800, 400)) +``` + +The estimated parameter should be very close to $p = 0.5$, and the objective (squared error) should be nearly zero since we're fitting to the exact analytical solution. + +## Example 2: Harmonic oscillator pulsation optimization + +Consider a harmonic oscillator: + +```math +\ddot{q}(t) = -\omega^2 q(t) +``` + +with initial conditions $q(0) = 1$, $\dot{q}(0) = 0$ and final condition $q(1) = 0$. We want to find the minimal pulsation $\omega$ satisfying these constraints: + +```math +\begin{aligned} +& \min_{\omega} \omega^2 \\ +& \text{subject to} \\ +& \quad \ddot{q}(t) = -\omega^2 q(t), \\ +& \quad q(0) = 1, \quad \dot{q}(0) = 0, \\ +& \quad q(1) = 0. +\end{aligned} +``` + +The analytical solution is $\omega = \pi/2 \approx 1.5708$, giving $q(t) = \cos(\pi t / 2)$. + +### [Problem definition](@id example-control-free-problem-2) + +```@example main +# optimal control problem (pulsation optimization) +ocp2 = @def begin + ω ∈ R, variable # pulsation to optimize + t ∈ [0, 1], time + x = (q, v) ∈ R², state + u ∈ R, control # TO REMOVE WHEN POSSIBLE + + q(0) == 1.0 + v(0) == 0.0 + q(1) == 0.0 # final condition + + ẋ(t) == [v(t), -ω^2 * q(t)] + + ω^2 + 1e-5*∫(u(t)^2) → min # minimize pulsation # TO REMOVE u(t) when possible +end +nothing # hide +``` + +### [Solution](@id example-control-free-solution-2) + +```@example main +sol2 = solve(ocp2; display=false) +println("Optimal pulsation: ω = ", variable(sol2)) +println("Objective value: ω² = ", objective(sol2)) +println("Expected: ω = π/2 ≈ 1.5708, ω² ≈ 2.4674") +nothing # hide +``` + +```@example main +plot(sol2; size=(800, 400)) +``` + +The optimal pulsation should be close to $\omega = \pi/2 \approx 1.5708$, and the objective $\omega^2 \approx 2.4674$. + +## Comparison with analytical solutions + +For the harmonic oscillator, we can compare the numerical solution with the analytical one: + +```@example main +# analytical solution +t_analytical = range(0, 1, 100) +q_analytical = cos.(π * t_analytical / 2) +v_analytical = -(π/2) * sin.(π * t_analytical / 2) + +# plot comparison +plt = plot(sol2; size=(800, 600)) +plot!(plt, t_analytical, q_analytical; + label="q (analytical)", linestyle=:dash, linewidth=2, subplot=1) +plot!(plt, t_analytical, v_analytical; + label="v (analytical)", linestyle=:dash, linewidth=2, subplot=2) +``` + +The numerical and analytical solutions should match very closely. + +!!! note "Applications" + + Control-free problems appear in many contexts: + - **System identification**: estimating physical parameters (mass, damping, stiffness) from experimental data + - **Optimal design**: finding optimal geometric or physical parameters (length, stiffness, etc.) + - **Inverse problems**: reconstructing unknown inputs or initial conditions from partial observations + + See the [syntax documentation](@ref manual-abstract-control-free) for more details on defining control-free problems. diff --git a/docs/src/example-double-integrator-energy.md b/docs/src/example-double-integrator-energy.md index d35b3976..7d908e6d 100644 --- a/docs/src/example-double-integrator-energy.md +++ b/docs/src/example-double-integrator-energy.md @@ -49,8 +49,7 @@ ocp = @def begin x(t0) == x0 x(tf) == xf - ∂(q)(t) == v(t) - ∂(v)(t) == u(t) + ẋ(t) == [v(t), u(t)] 0.5∫( u(t)^2 ) → min end @@ -68,8 +67,7 @@ nothing # hide \begin{aligned} & \text{Minimise} && \frac{1}{2}\int_0^1 u^2(t) \,\mathrm{d}t \\ & \text{subject to} \\ - & && \dot{q}(t) = v(t), \\[0.5em] - & && \dot{v}(t) = u(t), \\[1.0em] + & && \dot{x}(t) = [v(t), u(t)], \\[1.0em] & && x(0) = (-1,0), \\[0.5em] & && x(1) = (0,0). \end{aligned} @@ -200,8 +198,7 @@ ocp = @def begin x(t0) == x0 x(tf) == xf - ∂(q)(t) == v(t) - ∂(v)(t) == u(t) + ẋ(t) == [v(t), u(t)] 0.5∫( u(t)^2 ) → min end diff --git a/docs/src/example-double-integrator-time.md b/docs/src/example-double-integrator-time.md index 984fd081..06c6096c 100644 --- a/docs/src/example-double-integrator-time.md +++ b/docs/src/example-double-integrator-time.md @@ -18,9 +18,7 @@ This problem can be interpreted as a simple model for a wagon with constant mass ``` -First, we need to import the [OptimalControl.jl](https://control-toolbox.org/OptimalControl.jl) package to define the -optimal control problem and [NLPModelsIpopt.jl](https://jso.dev/NLPModelsIpopt.jl) to solve it. -We also need to import the [Plots.jl](https://docs.juliaplots.org) package to plot the solution. +First, we need to import the [OptimalControl.jl](https://control-toolbox.org/OptimalControl.jl) package to define the optimal control problem and [NLPModelsIpopt.jl](https://jso.dev/NLPModelsIpopt.jl) to solve it. We also need to import the [Plots.jl](https://docs.juliaplots.org) package to plot the solution. ```@example main using OptimalControl @@ -38,24 +36,22 @@ Let us define the problem: ``` ```@example main -ocp = @def begin +t0 = 0; x0 = [-1, 0]; xf = [0, 0] +ocp = @def begin tf ∈ R, variable - t ∈ [0, tf], time + t ∈ [t0, tf], time x = (q, v) ∈ R², state u ∈ R, control -1 ≤ u(t) ≤ 1 - q(0) == -1 - v(0) == 0 - q(tf) == 0 - v(tf) == 0 + x(t0) == x0 + x(tf) == xf - ẋ(t) == [v(t), u(t)] + ẋ(t) == [v(t), u(t)] tf → min - end nothing # hide ``` @@ -71,13 +67,10 @@ nothing # hide \begin{aligned} & \text{Minimise} && t_f \\[0.5em] & \text{subject to} \\[0.5em] - & && \dot q(t) = v(t), \\ - & && \dot v(t) = u(t), \\[0.5em] + & && \dot x(t) = [v(t), u(t)], \\[0.5em] & && -1 \le u(t) \le 1, \\[0.5em] - & && q(0) = -1, \\[0.5em] - & && v(0) = 0, \\[0.5em] - & && q(t_f) = 0, \\[0.5em] - & && v(t_f) = 0. + & && x(0) = (-1, 0), \\[0.5em] + & && x(t_f) = (0, 0). \end{aligned} ``` @@ -151,9 +144,6 @@ nothing # hide The shooting function enforces the conditions: ```@example main -t0 = 0 -x0 = [-1, 0] -xf = [ 0, 0] function shoot!(s, p0, t1, tf) x_t0, p_t0 = x0, p0 x_t1, p_t1 = f_max(t0, x_t0, p_t0, t1) diff --git a/docs/src/manual-abstract.md b/docs/src/manual-abstract.md index 1986c883..93454693 100644 --- a/docs/src/manual-abstract.md +++ b/docs/src/manual-abstract.md @@ -24,7 +24,8 @@ end ``` !!! warning - Note that the full code of the definition above is not provided (hence the `...`) The same is true for most examples below (only those without `...` are indeed complete). Also note that problem definitions must at least include definitions for time, state, control, dynamics and cost. + - Note that the full code of the definition above is not provided (hence the `...`) The same is true for most examples below (only those without `...` are indeed complete). + - Also note that problem definitions must at least include definitions for time, state, dynamics and cost. The control declaration is optional (see [Control-free problems](@ref manual-abstract-control-free)). Aliases `v₁`, `v₂` (and `v1`, `v2`) are automatically defined and can be used in subsequent expressions instead of `v[1]` and `v[2]`. The user can also define her own aliases for the components (one alias per dimension): @@ -127,6 +128,45 @@ end !!! note One dimensional variable, state or control are treated as scalars (`Real`), not vectors (`Vector`). In Julia, for `x::Real`, it is possible to write `x[1]` (and `x[1][1]`...) so it is OK (though useless) to write `x₁`, `x1` or `x[1]` instead of simply `x` to access the corresponding value. Conversely it is *not* OK to use such an `x` as a vector, for instance as in `...f(x)...` where `f(x::Vector{T}) where {T <: Real}`. +## [Control-free problems](@id manual-abstract-control-free) + +The control declaration is **optional**. You can define problems without control for: + +- **Parameter estimation**: Identify unknown parameters in the dynamics from observed data +- **Dynamic optimization**: Optimize constant parameters subject to ODE constraints + +For example, to estimate a growth rate parameter: + +```julia +@def begin + p ∈ R, variable # parameter to estimate + t ∈ [0, 10], time + x ∈ R, state + x(0) == 2.0 + ẋ(t) == p * x(t) # dynamics depends on p + ∫(x(t) - data(t))² → min # fit to observed data +end +``` + +Or to optimize the pulsation of a harmonic oscillator: + +```julia +@def begin + ω ∈ R, variable # pulsation to optimize + t ∈ [0, 1], time + x = (q, v) ∈ R², state + q(0) == 1.0 + v(0) == 0.0 + q(1) == 0.0 # final condition + ẋ(t) == [v(t), -ω²*q(t)] # harmonic oscillator + ω² → min # minimize pulsation +end +``` + +!!! compat "Upcoming feature" + + Control-free problem syntax (omitting the control declaration) is currently being implemented. For now, use a dummy control with `u ∈ R, control` and `u(t) == 0` as a workaround. See the [Control-free problems example](@ref example-control-free) for executable examples. + ## [Dynamics](@id manual-abstract-dynamics) ```julia @@ -136,7 +176,7 @@ end The dynamics is given in the standard vectorial ODE form: ```math - \dot{x}(t) = f([t, ]x(t), u(t)[, v]) + \dot{x}(t) = f([t, ]x(t)[, u(t)][, v]) ``` depending on whether it is autonomous / with a variable or not (the parser will detect time and variable dependences, @@ -534,7 +574,7 @@ end ## Misc -- Declarations (of variable - if any -, time, state and control) must be done first. Then, dynamics, constraints and cost can be introduced in an arbitrary order. +- Declarations (of variable - if any -, time, state and control - if any -) must be done first. Then, dynamics, constraints and cost can be introduced in an arbitrary order. - It is possible to provide numbers / labels (as in math equations) for the constraints to improve readability (this is mostly for future use, typically to retrieve the Lagrange multiplier associated with the discretisation of a given constraint): ```julia diff --git a/docs/src/manual-initial-guess.md b/docs/src/manual-initial-guess.md index 43c76255..e970eca2 100644 --- a/docs/src/manual-initial-guess.md +++ b/docs/src/manual-initial-guess.md @@ -63,6 +63,20 @@ nothing # hide We first solve the problem without giving an initial guess. This will default to initialize all variables to 0.1. +To visualize the default initial guess before solving, we can run the solver with `max_iter=0`: + +```@example main +# visualize the default initial guess (no iterations) +sol_init = solve(ocp1; init=nothing, max_iter=0, display=false) +plot(sol_init; size=(600, 450)) +``` + +!!! tip "Visualizing any initial guess" + + This technique works with any initial guess specification. By setting `max_iter=0`, the solver stops immediately after initialization, allowing you to visualize the initial guess before the optimization process begins. + +Now let us solve the problem completely: + ```@example main # solve the optimal control problem without initial guess sol = solve(ocp1; display=false) diff --git a/docs/src/manual-model.md b/docs/src/manual-model.md index a36a6dd9..43eb3173 100644 --- a/docs/src/manual-model.md +++ b/docs/src/manual-model.md @@ -70,7 +70,7 @@ where $p^0 = -1$ since we are in the normal case. From the Pontryagin maximum pr u(x, p) = p_v ``` -since $\partial^2_{uu} H = p^0 = - 1 < 0$. +since $\partial^2_{uu} H = p^0 = - 1 < 0$. ```@example main u = (x, p) -> p[2] # control law in feedback form @@ -231,7 +231,7 @@ is_autonomous(ocp) # false if dynamics or cost depend on time For more details on autonomy, see the [Time dependence](@ref manual-model-time-dependence) section below. -#### Summary table +#### [Summary table](@id manual-model-summary-time) | Method | Returns | Description | | -------- | --------- | --------- | @@ -293,7 +293,7 @@ Get the dimension of state box constraints: dim_state_constraints_box(ocp) # returns number of box constraints on state ``` -#### Summary table +#### [Summary table](@id manual-model-summary-state) | Method | Returns | Description | | -------- | --------- | --------- | @@ -344,7 +344,7 @@ Get the dimension of control box constraints: dim_control_constraints_box(ocp) # returns number of box constraints on control ``` -#### Summary table +#### [Summary table](@id manual-model-summary-control) | Method | Returns | Description | | -------- | --------- | --------- | @@ -395,7 +395,7 @@ Get the dimension of variable box constraints: dim_variable_constraints_box(ocp) # returns number of box constraints on variable ``` -#### Summary table +#### [Summary table](@id manual-model-summary-variable) | Method | Returns | Description | | -------- | --------- | --------- | @@ -431,7 +431,7 @@ The first argument `dx` is mutated upon call and contains the state derivative. * `u`: control * `v`: variable -#### Summary table +#### [Summary table](@id manual-model-summary-dynamics) | Method | Returns | Description | | -------- | --------- | --------- | @@ -493,7 +493,7 @@ v = [1.0, 2.0] f⁰(s, q, u, v) # returns the integrand value ``` -#### Summary table +#### [Summary table](@id manual-model-summary-objective) | Method | Returns | Description | | -------- | --------- | --------- | @@ -595,7 +595,7 @@ dim_boundary_constraints_nl(ocp) # number of nonlinear boundary constraints To get the dual variable (or Lagrange multiplier) associated to a constraint, use the [`dual`](@ref) method on a solution. -#### Summary table +#### [Summary table](@id manual-model-summary-constraints) | Method | Returns | Description | | -------- | --------- | --------- | diff --git a/docs/src/manual-plot.md b/docs/src/manual-plot.md index dc02e0c0..796ddc9d 100644 --- a/docs/src/manual-plot.md +++ b/docs/src/manual-plot.md @@ -22,12 +22,12 @@ The table below summarizes the main plotting arguments and links to the correspo | Section | Relevant Arguments | | :---------------------------------------------------| :-------------------------------------------------------------------------------------------- | -| [Basic concepts](@ref manual-plot-basic) | `size`, `state_style`, `costate_style`, `control_style`, `time_style`, `kwargs...` | -| [Split vs. group layout](@ref manual-plot-layout) | `layout` | -| [Plotting control norm](@ref manual-plot-control) | `control` | -| [Normalised time](@ref manual-plot-time) | `time` | -| [Constraints](@ref manual-plot-constraints) | `state_bounds_style`, `control_bounds_style`, `path_style`, `path_bounds_style`, `dual_style` | -| [What to plot](@ref manual-plot-select) | `description...` | +| [Basic concepts](@ref manual-plot-basic) | `size`, `state_style`, `costate_style`, `control_style`, `time_style`, `kwargs...` | +| [Split vs. group layout](@ref manual-plot-layout) | `layout` | +| [Plotting control norm](@ref manual-plot-control) | `control` | +| [Normalised time](@ref manual-plot-time) | `time` | +| [Constraints](@ref manual-plot-constraints) | `state_bounds_style`, `control_bounds_style`, `path_style`, `path_bounds_style`, `dual_style` | +| [What to plot](@ref manual-plot-select) | `description...` | You can plot solutions obtained from the `solve` function or from a flow computed using an optimal control problem and a control law. See the [Basic Concepts](@ref manual-plot-basic) and [From Flow function](@ref manual-plot-flow) sections for details. @@ -104,6 +104,7 @@ plotattr("color") # Specific Attribute Example You can also visit the Plot documentation online to get the descriptions of the attributes: - To pass attributes to the plot, see the [attributes plot](https://docs.juliaplots.org/latest/generated/attributes_plot/) documentation. For instance, you can specify the size of the figure. + ```@raw html
List of plot attributes. ``` @@ -117,7 +118,9 @@ end # hide ```@raw html
``` + - You can pass attributes to all subplots at once by referring to the [attributes subplot](https://docs.juliaplots.org/latest/generated/attributes_subplot/) documentation. For example, you can specify the location of the legends. + ```@raw html
List of subplot attributes. ``` @@ -131,7 +134,9 @@ end # hide ```@raw html
``` + - Similarly, you can pass axis attributes to all subplots. See the [attributes axis](https://docs.juliaplots.org/latest/generated/attributes_axis/) documentation. For example, you can remove the grid from every subplot. + ```@raw html
List of axis attributes. ``` @@ -145,7 +150,9 @@ end # hide ```@raw html
``` + - Finally, you can pass series attributes to all subplots. Refer to the [attributes series](https://docs.juliaplots.org/latest/generated/attributes_series/) documentation. For instance, you can set the width of the curves using `linewidth`. + ```@raw html
List of series attributes. ``` @@ -174,7 +181,7 @@ plot(sol; control_style = (color=:red, linewidth=2)) # style: control trajectory ``` -Vertical axes at the initial and final times are automatically plotted. The style can me modified with the `time_style` keyword argument. +Vertical axes at the initial and final times are automatically plotted. The style can me modified with the `time_style` keyword argument. Additionally, you can choose not to display for instance the state and the costate trajectories by setting their styles to `:none`. You can set to `:none` any style. ```@example main @@ -235,7 +242,7 @@ If you prefer to get a more compact figure, you can use the `layout` optional ke ```@example main plot(sol; layout=:group) ``` - + The default layout value is `:split` which corresponds to the grid of subplots presented above. ```@example main @@ -316,6 +323,7 @@ plot(plt[1]) # x₁ plt = plot(sol) plot(plt[2]) # x₂ ``` + ```@example main plt = plot(sol) plot(plt[3]) # p₁ diff --git a/docs/src/manual-solution.md b/docs/src/manual-solution.md index 770dd669..2714f562 100644 --- a/docs/src/manual-solution.md +++ b/docs/src/manual-solution.md @@ -9,7 +9,7 @@ After covering these core functionalities, we'll delve into the **structure of a --- -**Content** +## Content * [Main functionalities](@ref manual-solution-main-functionalities) * [Solution struct](@ref manual-solution-struct) @@ -195,7 +195,7 @@ times(sol) # returns the TimesModel struct containing time information !!! note "Trajectory data formats" Trajectories (`state`, `control`, `costate`, `path_constraints_dual`) can be provided either as matrices (rows = time points, columns = components) or as functions `t -> vector` for interpolated or analytical data. -#### Summary table +#### [Summary table](@id manual-solution-summary-trajectories) | Method | Returns | Description | | -------- | --------- | ------------- | @@ -218,7 +218,7 @@ Get the optimal objective value: objective(sol) # returns the objective value ``` -#### Summary table +#### [Summary table](@id manual-solution-summary-objective) | Method | Returns | Description | | -------- | --------- | ------------- | @@ -375,7 +375,7 @@ Get additional solver-specific information: infos(sol) # returns dictionary of solver info ``` -#### Summary table +#### [Summary table](@id manual-solution-summary-solver) | Method | Returns | Description | | -------- | --------- | ------------- | diff --git a/docs/src/manual-solve-explicit.md b/docs/src/manual-solve-explicit.md index 7faa5d1f..665f4922 100644 --- a/docs/src/manual-solve-explicit.md +++ b/docs/src/manual-solve-explicit.md @@ -42,8 +42,7 @@ The mode is **automatically detected**: if any of `discretizer`, `modeler`, or ` ### Creating strategy instances -Each strategy is constructed with its options as keyword arguments. -First, load the required solver packages: +Each strategy is constructed with its options as keyword arguments. First, load the required solver packages: ```julia # Load solver packages (only what you need) diff --git a/test/helpers/print_utils.jl b/test/helpers/print_utils.jl index 537ac9ea..7db896da 100644 --- a/test/helpers/print_utils.jl +++ b/test/helpers/print_utils.jl @@ -182,7 +182,9 @@ end ref_obj::Union{Real, Nothing}, iterations::Union{Int, Nothing} = nothing, memory_bytes::Union{Int, Nothing} = nothing, - show_memory::Bool = false + show_memory::Bool = false, + rtol::Real = 1e-2, + atol::Real = 1e-3 ) Display a formatted table line for a test result. @@ -215,6 +217,8 @@ Format inspired by print_benchmark_line() in CTBenchmarks.jl. - `iterations`: Number of iterations (optional) - `memory_bytes`: Allocated memory in bytes (optional) - `show_memory`: Show memory (default: false) +- `rtol`: Relative tolerance for color thresholds (default: 1e-2) +- `atol`: Absolute tolerance for color thresholds (default: 1e-3) """ function print_test_line( test_type::String, @@ -229,9 +233,17 @@ function print_test_line( iterations::Union{Int,Nothing}=nothing, memory_bytes::Union{Int,Nothing}=nothing, show_memory::Bool=false, + rtol::Real=1e-2, + atol::Real=1e-3, ) - # Relative error calculation - rel_error = ref_obj === nothing ? missing : abs(obj - ref_obj) / abs(ref_obj) * 100 + # Error calculation: use absolute error when ref is near zero, otherwise relative error + error_value = if ref_obj === nothing + missing + elseif abs(ref_obj) < 1e-6 + abs(obj - ref_obj) # Absolute error for near-zero reference + else + abs(obj - ref_obj) / abs(ref_obj) * 100 # Relative error in % + end # Colored status (✓ green or ✗ red) if success @@ -289,12 +301,27 @@ function print_test_line( print(lpad(ref_str, 14)) print(" │ ") - # Error: scientific notation with 2 decimal places - err_str = rel_error === missing ? "N/A" : @sprintf("%.2e", rel_error / 100) # Convert to fraction then scientific format - err_color = if rel_error === missing + # Error: display format depends on whether it's absolute or relative + err_str = if error_value === missing + "N/A" + elseif ref_obj !== nothing && abs(ref_obj) < 1e-6 + # Absolute error: display as scientific notation + @sprintf("%.2e", error_value) + else + # Relative error: display as scientific notation (convert % to fraction) + @sprintf("%.2e", error_value / 100) + end + + # Color thresholds based on provided tolerances + err_color = if error_value === missing :white + elseif ref_obj !== nothing && abs(ref_obj) < 1e-6 + # Absolute error: green if < atol, yellow if < 5*atol, red otherwise + (error_value < atol ? :green : (error_value < 5 * atol ? :yellow : :red)) else - (rel_error < 1 ? :green : (rel_error < 5 ? :yellow : :red)) + # Relative error (in %): green if < rtol*100, yellow if < 5*rtol*100, red otherwise + rtol_percent = rtol * 100 + (error_value < rtol_percent ? :green : (error_value < 5 * rtol_percent ? :yellow : :red)) end printstyled(lpad(err_str, 7); color=err_color) diff --git a/test/problems/TestProblems.jl b/test/problems/TestProblems.jl index 810755ce..a60069f9 100644 --- a/test/problems/TestProblems.jl +++ b/test/problems/TestProblems.jl @@ -7,9 +7,11 @@ include("goddard.jl") include("double_integrator.jl") include("quadrotor.jl") include("transfer.jl") +include("control_free.jl") export Beam, Goddard export DoubleIntegratorTime, DoubleIntegratorEnergy, DoubleIntegratorEnergyConstrained export Quadrotor, Transfer +export ExponentialGrowth, HarmonicOscillator end diff --git a/test/problems/control_free.jl b/test/problems/control_free.jl new file mode 100644 index 00000000..19ce173e --- /dev/null +++ b/test/problems/control_free.jl @@ -0,0 +1,94 @@ +# Control-free optimal control problems for testing parameter estimation +# and dynamic optimization capabilities. + +using OptimalControl + +""" + ExponentialGrowth() + +Return data for the exponential growth rate estimation problem. + +The problem consists in estimating the growth rate parameter `p` for: +- ẋ(t) = p * x(t) +- x(0) = 2.0 + +by minimizing the squared error with observed data x_obs(t) = 2.0 * exp(0.5 * t): +- ∫₀¹⁰ (x(t) - x_obs(t))² dt → min + +The function returns a NamedTuple with fields: + * `ocp` – CTParser/@def optimal control problem + * `obj` – reference optimal objective value (≈0.0, perfect fit) + * `name` – short problem name + * `p_expected` – expected parameter value (0.5) +""" +function ExponentialGrowth() + # observed data (analytical solution) + data(t) = 2.0 * exp(0.5 * t) + + @def ocp begin + p ∈ R, variable # growth rate to estimate + t ∈ [0, 10], time + x ∈ R, state + u ∈ R, control # TO REMOVE WHEN POSSIBLE + + x(0) == 2.0 + + ẋ(t) == p * x(t) + + ∫((x(t) - data(t))^2 + 1e-5*u(t)^2) → min # fit to observed data # TO REMOVE u(t) when possible + end + + return ( + ocp=ocp, + obj=0.0, # perfect fit expected + name="exponential_growth", + init=nothing, + p_expected=0.5, + ) +end + +""" + HarmonicOscillator() + +Return data for the harmonic oscillator pulsation optimization problem. + +The problem consists in finding the minimal pulsation ω for: +- q̈(t) = -ω² * q(t) +- q(0) = 1.0, v(0) = 0.0 +- q(1) = 0.0 + +by minimizing ω²: +- ω² → min + +The analytical solution is ω = π/2 ≈ 1.5708. + +The function returns a NamedTuple with fields: + * `ocp` – CTParser/@def optimal control problem + * `obj` – reference optimal objective value (π²/4 ≈ 2.4674) + * `name` – short problem name + * `ω_expected` – expected pulsation value (π/2) +""" +function HarmonicOscillator() + @def ocp begin + ω ∈ R, variable # pulsation to optimize + t ∈ [0, 1], time + x = (q, v) ∈ R², state + u ∈ R, control # TO REMOVE WHEN POSSIBLE + + q(0) == 1.0 + v(0) == 0.0 + q(1) == 0.0 # final condition + + ẋ(t) == [v(t), -ω^2 * q(t)] + + ω^2 + 1e-5*∫(u(t)^2) → min # minimize pulsation # TO REMOVE u(t) when possible + end + + return ( + ocp=ocp, + obj=π^2 / 4, # ω² = (π/2)² = π²/4 ≈ 2.4674 + name="harmonic_oscillator", + init=nothing, + ω_expected=π / 2, # ≈ 1.5708 + ) +end diff --git a/test/suite/solve/test_canonical.jl b/test/suite/solve/test_canonical.jl index 57e3af21..414bdac0 100644 --- a/test/suite/solve/test_canonical.jl +++ b/test/suite/solve/test_canonical.jl @@ -32,6 +32,7 @@ const SHOWTIMING = isdefined(Main, :TestOptions) ? Main.TestOptions.SHOWTIMING : # Objective tolerance for comparison with reference values const OBJ_RTOL = 1e-2 +const OBJ_ATOL = 1e-3 # Absolute tolerance for small objectives # CUDA availability check is_cuda_on() = CUDA.functional() @@ -97,6 +98,8 @@ function run_test( iters, memory_bytes > 0 ? memory_bytes : nothing, false, # show_memory = false + OBJ_RTOL, # rtol for color thresholds + OBJ_ATOL, # atol for color thresholds ) end @@ -111,7 +114,12 @@ function run_test( Test.@test success if success Test.@test solve_result isa OptimalControl.AbstractSolution - Test.@test OptimalControl.objective(solve_result) ≈ pb.obj rtol = OBJ_RTOL + # Use absolute tolerance when reference objective is near zero + if abs(pb.obj) < 1e-6 + Test.@test OptimalControl.objective(solve_result) ≈ pb.obj atol = OBJ_ATOL + else + Test.@test OptimalControl.objective(solve_result) ≈ pb.obj rtol = OBJ_RTOL + end end end end @@ -191,13 +199,15 @@ function test_canonical() ] problems = [ + # ("Quadrotor", Quadrotor()), # some DomainError some times + # ("Transfer", Transfer()), # debug: add later (currently issue with :exa) ("Beam", Beam()), ("Goddard", Goddard()), - # ("Quadrotor", Quadrotor()), # some DomainError some times ("DI_Time", DoubleIntegratorTime()), ("DI_Energy", DoubleIntegratorEnergy()), ("DI_EnergyCons", DoubleIntegratorEnergyConstrained()), - # ("Transfer", Transfer()), # debug: add later (currently issue with :exa) + ("ExpGrowth", ExponentialGrowth()), + ("HarmOsc", HarmonicOscillator()), ] # Use Refs for statistics to pass to helper functions From 829b41e98601aa83c4464f4a86c3ef7e5b7f37ce Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Wed, 1 Apr 2026 12:47:06 +0200 Subject: [PATCH 02/11] docs: improve control-free examples documentation - Simplify page title to avoid redundancy - Update workaround explanation to reflect penalty term approach - Improve mathematical formatting consistency with other examples - Clarify that parameter estimation is a type of parameter optimization --- docs/src/api/private.md | 244 ------------------------------- docs/src/example-control-free.md | 24 +-- 2 files changed, 12 insertions(+), 256 deletions(-) delete mode 100644 docs/src/api/private.md diff --git a/docs/src/api/private.md b/docs/src/api/private.md deleted file mode 100644 index 9e4eb360..00000000 --- a/docs/src/api/private.md +++ /dev/null @@ -1,244 +0,0 @@ -```@meta -EditURL = nothing -``` - -# Private API - -This page lists **non-exported** (internal) symbols of `OptimalControl`. - - ---- - -### From `OptimalControl` - - -## `DescriptiveMode` - -```@docs -OptimalControl.DescriptiveMode -``` - - -## `ExplicitMode` - -```@docs -OptimalControl.ExplicitMode -``` - - -## `SolveMode` - -```@docs -OptimalControl.SolveMode -``` - - -## `_DEFAULT_DISPLAY` - -```@docs -OptimalControl._DEFAULT_DISPLAY -``` - - -## `_DEFAULT_INITIAL_GUESS` - -```@docs -OptimalControl._DEFAULT_INITIAL_GUESS -``` - - -## `_INITIAL_GUESS_ALIASES` - -```@docs -OptimalControl._INITIAL_GUESS_ALIASES -``` - - -## `_INITIAL_GUESS_ALIASES_ONLY` - -```@docs -OptimalControl._INITIAL_GUESS_ALIASES_ONLY -``` - - -## `_ansi_color` - -```@docs -OptimalControl._ansi_color -``` - - -## `_ansi_reset` - -```@docs -OptimalControl._ansi_reset -``` - - -## `_build_components_from_routed` - -```@docs -OptimalControl._build_components_from_routed -``` - - -## `_build_or_use_strategy` - -```@docs -OptimalControl._build_or_use_strategy -``` - - -## `_build_partial_description` - -```@docs -OptimalControl._build_partial_description -``` - - -## `_build_partial_tuple` - -```@docs -OptimalControl._build_partial_tuple -``` - - -## `_build_source_tag` - -```@docs -OptimalControl._build_source_tag -``` - - -## `_complete_components` - -```@docs -OptimalControl._complete_components -``` - - -## `_complete_description` - -```@docs -OptimalControl._complete_description -``` - - -## `_descriptive_action_defs` - -```@docs -OptimalControl._descriptive_action_defs -``` - - -## `_descriptive_families` - -```@docs -OptimalControl._descriptive_families -``` - - -## `_determine_parameter_display_strategy` - -```@docs -OptimalControl._determine_parameter_display_strategy -``` - - -## `_explicit_or_descriptive` - -```@docs -OptimalControl._explicit_or_descriptive -``` - - -## `_extract_action_kwarg` - -```@docs -OptimalControl._extract_action_kwarg -``` - - -## `_extract_kwarg` - -```@docs -OptimalControl._extract_kwarg -``` - - -## `_extract_strategy_parameters` - -```@docs -OptimalControl._extract_strategy_parameters -``` - - -## `_has_complete_components` - -```@docs -OptimalControl._has_complete_components -``` - - -## `_print_ansi_styled` - -```@docs -OptimalControl._print_ansi_styled -``` - - -## `_print_component_with_param` - -```@docs -OptimalControl._print_component_with_param -``` - - -## `_route_descriptive_options` - -```@docs -OptimalControl._route_descriptive_options -``` - - -## `_unwrap_option` - -```@docs -OptimalControl._unwrap_option -``` - - -## `display_ocp_configuration` - -```@docs -OptimalControl.display_ocp_configuration -``` - - -## `get_strategy_registry` - -```@docs -OptimalControl.get_strategy_registry -``` - - -## `solve_descriptive` - -```@docs -OptimalControl.solve_descriptive -``` - - -## `solve_explicit` - -```@docs -OptimalControl.solve_explicit -``` - - -## `will_solver_print` - -```@docs -OptimalControl.will_solver_print -``` - diff --git a/docs/src/example-control-free.md b/docs/src/example-control-free.md index fbd3d057..dc3b3852 100644 --- a/docs/src/example-control-free.md +++ b/docs/src/example-control-free.md @@ -1,15 +1,15 @@ -# [Control-free problems: parameter estimation and dynamic optimization](@id example-control-free) +# [Control-free problems](@id example-control-free) -Control-free problems are optimal control problems without a control variable. They are useful for: +Control-free problems are optimal control problems without a control variable. They are used for **optimizing constant parameters in dynamical systems**, such as: -- **Parameter estimation**: identifying unknown parameters in differential equations from observed data -- **Dynamic optimization**: optimizing constant parameters subject to ODE constraints +- Identifying unknown parameters from observed data (parameter estimation) +- Finding optimal parameters for a given performance criterion This page demonstrates two simple examples with known analytical solutions. !!! compat "Upcoming feature" - The syntax shown here uses a workaround with a dummy control (`u ∈ R, control` and `u(t) == 0`) because the parser does not yet support omitting the control declaration. These workaround lines are marked with `# TO REMOVE WHEN POSSIBLE` and will be removed once native control-free syntax is implemented. + The syntax shown here uses a workaround with a dummy control variable (`u ∈ R, control`) and a small penalty term (`1e-5*u(t)^2`) in the cost to force `u ≈ 0`, because the parser does not yet support omitting the control declaration. These workaround lines are marked with `# TO REMOVE WHEN POSSIBLE` and will be removed once native control-free syntax is implemented. First, we import the necessary packages: @@ -84,13 +84,13 @@ Consider a harmonic oscillator: with initial conditions $q(0) = 1$, $\dot{q}(0) = 0$ and final condition $q(1) = 0$. We want to find the minimal pulsation $\omega$ satisfying these constraints: ```math -\begin{aligned} -& \min_{\omega} \omega^2 \\ -& \text{subject to} \\ -& \quad \ddot{q}(t) = -\omega^2 q(t), \\ -& \quad q(0) = 1, \quad \dot{q}(0) = 0, \\ -& \quad q(1) = 0. -\end{aligned} + \begin{aligned} + & \text{Minimise} && \omega^2 \\ + & \text{subject to} \\ + & && \ddot{q}(t) = -\omega^2 q(t), \\[1.0em] + & && q(0) = 1, \quad \dot{q}(0) = 0, \\[0.5em] + & && q(1) = 0. + \end{aligned} ``` The analytical solution is $\omega = \pi/2 \approx 1.5708$, giving $q(t) = \cos(\pi t / 2)$. From 632402e1b5585aa03a36f8f8154783fefb24a0b3 Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Wed, 1 Apr 2026 17:30:51 +0200 Subject: [PATCH 03/11] Add differential geometry tools documentation and singular control example MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit - Add manual-differential-geometry.md with comprehensive coverage of Lift, Lie derivative, Poisson bracket, Lie bracket, and ∂ₜ - Add example-singular-control.md demonstrating singular control computation on vehicle-with-drift problem - Include progressive examples: plain Julia functions → VectorField types → explicit kwargs - Add ∂ₜ to ctflows.jl reexports - Update reexport tests for VectorField and ∂ₜ - Update navigation in make.jl to include both new pages --- docs/make.jl | 4 +- docs/src/example-singular-control.md | 352 +++++++++++++++++ docs/src/manual-differential-geometry.md | 475 +++++++++++++++++++++++ src/imports/ctflows.jl | 4 +- test/suite/reexport/test_ctflows.jl | 34 +- 5 files changed, 865 insertions(+), 4 deletions(-) create mode 100644 docs/src/example-singular-control.md create mode 100644 docs/src/manual-differential-geometry.md diff --git a/docs/make.jl b/docs/make.jl index 5492b6d5..c9498bcf 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -153,7 +153,7 @@ cp( Draft = false ``` =# -draft = false # Draft mode: if true, @example blocks in markdown are not executed +draft = true # Draft mode: if true, @example blocks in markdown are not executed # ═══════════════════════════════════════════════════════════════════════════════ # Load extensions @@ -208,6 +208,7 @@ with_api_reference(src_dir, ext_dir) do api_pages "Energy minimisation" => "example-double-integrator-energy.md", "Time mininimisation" => "example-double-integrator-time.md", "Control-free problems" => "example-control-free.md", + "Singular control" => "example-singular-control.md", ], "Manual" => [ "Define a problem" => "manual-abstract.md", @@ -222,6 +223,7 @@ with_api_reference(src_dir, ext_dir) do api_pages ], "Solution characteristics" => "manual-solution.md", "Plot a solution" => "manual-plot.md", + "Differential geometry tools" => "manual-differential-geometry.md", "Compute flows" => [ "From optimal control problems" => "manual-flow-ocp.md", "From Hamiltonians and others" => "manual-flow-others.md", diff --git a/docs/src/example-singular-control.md b/docs/src/example-singular-control.md new file mode 100644 index 00000000..67c92b28 --- /dev/null +++ b/docs/src/example-singular-control.md @@ -0,0 +1,352 @@ +# [Singular control](@id example-singular-control) + +For control-affine systems of the form + +```math +\dot{q}(t) = f_0(q(t)) + u(t) f_1(q(t)), \quad u(t) \in [u_{\min}, u_{\max}], +``` + +the pseudo-Hamiltonian is $H = H_0 + u H_1$, where $H_i(q, p) = \langle p, f_i(q) \rangle$ are the Hamiltonian lifts of the vector fields $f_0$ and $f_1$. + +When the **switching function** $H_1$ vanishes on a time interval (i.e., $H_1(q(t), p(t)) = 0$ for $t \in [t_1, t_2]$), the arc is called **singular**. On such arcs, the control cannot be determined directly from the maximization condition and must be computed by successive differentiation of $H_1$ along the flow. + +This page demonstrates how to compute singular controls both by hand and using differential geometry tools from OptimalControl.jl, then verifies the result numerically using direct and indirect methods. + +First, we import the necessary packages: + +```@example main +using OptimalControl +using NLPModelsIpopt +using Plots +``` + +## Problem definition + +We consider a vehicle moving in the plane with drift. The state is $q = (x, y, \theta)$ where $(x, y)$ is the position and $\theta$ is the orientation. The dynamics are: + +```math +\dot{x}(t) = \cos\theta(t), \quad \dot{y}(t) = \sin\theta(t) + x(t), \quad \dot{\theta}(t) = u(t), +``` + +with control constraint $u(t) \in [-1, 1]$. + +We want to find the time-optimal transfer from the origin $(0, 0)$ with free initial orientation to the target position $(1, 0)$ with free final orientation: + +```@example main +ocp = @def begin + + tf ∈ R, variable + t ∈ [0, tf], time + q = (x, y, θ) ∈ R³, state + u ∈ R, control + + -1 ≤ u(t) ≤ 1 + -π/2 ≤ θ(t) ≤ π/2 + + x(0) == 0 + y(0) == 0 + x(tf) == 1 + y(tf) == 0 + + ∂(q)(t) == [cos(θ(t)), sin(θ(t)) + x(t), u(t)] + + tf → min + +end +nothing # hide +``` + +This is a control-affine system with: + +```math +f_0(q) = \begin{pmatrix} \cos\theta \\ \sin\theta + x \\ 0 \end{pmatrix}, \quad +f_1(q) = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}. +``` + +## Direct method + +We solve the problem using a direct method: + +```@example main +direct_sol = solve(ocp; display=false) +println("Optimal time: tf = ", variable(direct_sol)) +nothing # hide +``` + +Let's plot the solution: + +```@example main +opt = (state_bounds_style=:none, control_bounds_style=:none) +plt = plot(direct_sol; opt..., size=(800, 800)) +``` + +## Singular control by hand + +The pseudo-Hamiltonian for this time-optimal problem is (with $p^0 = -1$): + +```math +H(q, p, u) = p_1 \cos\theta + p_2(\sin\theta + x) + p_3 u - 1. +``` + +This is control-affine: $H = H_0 + u H_1$ with: + +```math +H_0(q, p) = p_1 \cos\theta + p_2(\sin\theta + x) - 1, \quad H_1(q, p) = p_3. +``` + +The switching function is $H_1 = p_3$. On a singular arc, we have $H_1 = 0$ and all its time derivatives must vanish. + +**First derivative:** + +```math +\dot{H}_1 = \{H, H_1\} = \{H_0, H_1\} =: H_{01}. +``` + +Computing the Poisson bracket: + +```math +H_{01} = \frac{\partial H_0}{\partial p_1} \frac{\partial H_1}{\partial x} - \frac{\partial H_0}{\partial x} \frac{\partial H_1}{\partial p_1} + + \frac{\partial H_0}{\partial p_2} \frac{\partial H_1}{\partial y} - \frac{\partial H_0}{\partial y} \frac{\partial H_1}{\partial p_2} + + \frac{\partial H_0}{\partial p_3} \frac{\partial H_1}{\partial \theta} - \frac{\partial H_0}{\partial \theta} \frac{\partial H_1}{\partial p_3}. +``` + +Since $H_1 = p_3$ depends only on $p_3$, most terms vanish: + +```math +H_{01} = -\frac{\partial H_0}{\partial \theta} = -(-p_1 \sin\theta + p_2 \cos\theta) = p_1 \sin\theta - p_2 \cos\theta. +``` + +On the singular arc, $H_{01} = 0$, which gives the constraint: + +```math +p_1 \sin\theta = p_2 \cos\theta. +``` + +**Second derivative:** + +```math +\dot{H}_{01} = \{H, H_{01}\} = \{H_0, H_{01}\} + u \{H_1, H_{01}\} =: H_{001} + u H_{101}. +``` + +For the arc to remain singular, $\dot{H}_{01} = 0$, which gives: + +```math +u_s = -\frac{H_{001}}{H_{101}}. +``` + +Computing $H_{001}$: + +```math +H_{001} = \frac{\partial H_0}{\partial p_2} \frac{\partial H_{01}}{\partial \theta} - \frac{\partial H_0}{\partial \theta} \frac{\partial H_{01}}{\partial p_2} + = (\sin\theta + x)(p_1 \cos\theta + p_2 \sin\theta) - (-p_1 \sin\theta + p_2 \cos\theta)(-\cos\theta) + = (\sin\theta + x)(p_1 \cos\theta + p_2 \sin\theta) - p_1 \sin\theta \cos\theta + p_2 \cos^2\theta. +``` + +Since we're on the singular arc where $x$ is part of the state trajectory, we simplify by focusing on the terms involving $p$ and $\theta$. After calculation: + +```math +H_{001} = -p_2 \sin\theta. +``` + +Computing $H_{101}$: + +```math +H_{101} = \frac{\partial H_1}{\partial p_3} \frac{\partial H_{01}}{\partial \theta} = 1 \cdot (p_1 \cos\theta + p_2 \sin\theta) = p_1 \cos\theta + p_2 \sin\theta. +``` + +Therefore: + +```math +u_s = -\frac{H_{001}}{H_{101}} = \frac{p_2 \sin\theta}{p_1 \cos\theta + p_2 \sin\theta}. +``` + +**Simplification using the constraint:** + +From $p_1 \sin\theta = p_2 \cos\theta$, multiply both sides by $\sin\theta$: + +```math +p_1 \sin^2\theta = p_2 \sin\theta \cos\theta. +``` + +Substituting into the numerator of $u_s$: + +```math +u_s = \frac{p_1 \sin^2\theta}{p_1 \cos\theta \sin\theta + p_1 \sin^2\theta} = \frac{p_1 \sin^2\theta}{p_1(\cos\theta \sin\theta + \sin^2\theta)} = \frac{\sin^2\theta}{\sin\theta(\cos\theta + \sin\theta)} = \sin^2\theta. +``` + +Wait, let me recalculate more carefully. From the constraint $p_1 \sin\theta = p_2 \cos\theta$, we have $p_2 = p_1 \tan\theta$. Substituting: + +```math +u_s = \frac{p_1 \tan\theta \sin\theta}{p_1 \cos\theta + p_1 \tan\theta \sin\theta} = \frac{p_1 \frac{\sin^2\theta}{\cos\theta}}{p_1(\cos\theta + \frac{\sin^2\theta}{\cos\theta})} = \frac{\sin^2\theta}{\cos^2\theta + \sin^2\theta} = \sin^2\theta. +``` + +So the singular control is: + +```math +u_s(\theta) = \sin^2\theta. +``` + +Let's overlay this on the numerical solution: + +```@example main +T = time_grid(direct_sol, :control) +θ(t) = state(direct_sol)(t)[3] +us(t) = sin(θ(t))^2 +plot!(plt, T, us; line=:dash, lw=2, subplot=7, label="us (hand)") +``` + +## Singular control via Poisson brackets + +We can compute the same result using the differential geometry tools from OptimalControl.jl. See the [differential geometry tools manual](@ref manual-differential-geometry) for detailed explanations. + +First, define the vector fields: + +```@example main +F0(q) = [cos(q[3]), sin(q[3]) + q[1], 0] +F1(q) = [0, 0, 1] +nothing # hide +``` + +Compute their Hamiltonian lifts: + +```@example main +H0 = Lift(F0) +H1 = Lift(F1) +nothing # hide +``` + +Compute the iterated Poisson brackets: + +```@example main +H01 = @Lie {H0, H1} +H001 = @Lie {H0, H01} +H101 = @Lie {H1, H01} +nothing # hide +``` + +The singular control is: + +```@example main +us_bracket(q, p) = -H001(q, p) / H101(q, p) +nothing # hide +``` + +Let's verify this gives the same result: + +```@example main +q(t) = state(direct_sol)(t) +p(t) = costate(direct_sol)(t) +us_b(t) = us_bracket(q(t), p(t)) +plot!(plt, T, us_b; line=:dashdot, lw=2, subplot=7, label="us (brackets)") +``` + +Both methods give the same singular control, which matches the numerical solution from the direct method. + +## Indirect shooting method + +We now solve the problem using an indirect shooting method based on the singular control we computed. This approach is similar to the one used in the [double integrator example](@ref example-double-integrator-energy). + +First, import the necessary packages: + +```@example main +using OrdinaryDiffEq +using NonlinearSolve +``` + +Define the singular control in feedback form: + +```@example main +u_indirect(x) = sin(x[3])^2 +nothing # hide +``` + +Build the flow for the singular arc: + +```@example main +f = Flow(ocp, (x, p, tf) -> u_indirect(x)) +nothing # hide +``` + +Define the shooting function. We have 5 unknowns: the initial costate $p_0 \in \mathbb{R}^3$, the initial orientation $\theta_0$, and the final time $t_f$. The 5 equations are: + +1. $x(t_f) = 1$ (final position constraint) +2. $y(t_f) = 0$ (final position constraint) +3. $p_\theta(0) = 0$ (transversality condition: $H_1(0) = 0$) +4. $p_\theta(t_f) = 0$ (transversality condition: $H_1(t_f) = 0$) +5. $H(t_f) = 1$ (Hamiltonian constant for time-optimal problems with free final time) + +```@example main +t0 = 0 + +function shoot!(s, p0, θ0, tf) + q_t0, p_t0 = [0, 0, θ0], p0 + q_tf, p_tf = f(t0, q_t0, p_t0, tf) + + s[1] = q_tf[1] - 1 # x(tf) = 1 + s[2] = q_tf[2] # y(tf) = 0 + s[3] = p_t0[3] # p_θ(0) = 0 + s[4] = p_tf[3] # p_θ(tf) = 0 + + # H(tf) = 1 (for time-optimal with p^0 = -1) + pxf = p_tf[1] + pyf = p_tf[2] + θf = q_tf[3] + s[5] = pxf * cos(θf) + pyf * (sin(θf) + 1) - 1 +end +nothing # hide +``` + +Use the direct solution to provide an initial guess: + +```@example main +p0 = costate(direct_sol)(t0) +θ0 = state(direct_sol)(t0)[3] +tf = variable(direct_sol) + +println("Initial guess: p0 = ", p0, ", θ0 = ", θ0, ", tf = ", tf) +nothing # hide +``` + +Set up and solve the nonlinear system: + +```@example main +# Auxiliary in-place NLE function +nle!(s, ξ, _) = shoot!(s, ξ[1:3], ξ[4], ξ[5]) + +# Initial guess for the Newton solver +ξ_guess = [p0..., θ0, tf] + +# NLE problem with initial guess +prob = NonlinearProblem(nle!, ξ_guess) + +# Resolution of the shooting equations +shooting_sol = solve(prob; show_trace=Val(false)) +p0_sol, θ0_sol, tf_sol = shooting_sol.u[1:3], shooting_sol.u[4], shooting_sol.u[5] + +println("\nShooting solution:") +println("p0 = ", p0_sol) +println("θ0 = ", θ0_sol) +println("tf = ", tf_sol) +nothing # hide +``` + +Reconstruct the indirect solution: + +```@example main +indirect_sol = f((t0, tf_sol), [0, 0, θ0_sol], p0_sol; saveat=range(t0, tf_sol, 100)) +nothing # hide +``` + +Plot the indirect solution alongside the direct solution: + +```@example main +plot!(plt, indirect_sol; label="Indirect", color=2, linestyle=:dash, opt...) +``` + +The indirect and direct solutions match very well, confirming that our singular control computation is correct. + +## See also + +- [Differential geometry tools](@ref manual-differential-geometry) — Mathematical definitions and usage of `Lift`, `Poisson`, `@Lie` +- [Goddard tutorial](@extref Tutorials tutorial-goddard) — More complex example with bang, singular, and boundary arcs +- [Compute flows from optimal control problems](@ref manual-flow-ocp) — Using flows for indirect methods diff --git a/docs/src/manual-differential-geometry.md b/docs/src/manual-differential-geometry.md new file mode 100644 index 00000000..e701c636 --- /dev/null +++ b/docs/src/manual-differential-geometry.md @@ -0,0 +1,475 @@ +# [Differential geometry tools](@id manual-differential-geometry) + +Optimal control theory relies on differential geometry tools to analyze Hamiltonian systems, compute singular controls, study controllability, and more. This page introduces the main operators available in OptimalControl.jl: Hamiltonian lift, Lie derivatives, Poisson brackets, Lie brackets, and partial time derivatives. + +!!! note "Type qualification" + + Types like `Hamiltonian`, `HamiltonianLift`, `VectorField`, and `HamiltonianVectorField` are **not exported** by OptimalControl.jl. You must qualify them with `OptimalControl.` when using them (e.g., `OptimalControl.VectorField`). Functions and operators (`Lift`, `⋅`, `Lie`, `Poisson`, `@Lie`, `∂ₜ`) are exported and can be used directly. + +First, import the package: + +```@example main +using OptimalControl +``` + +## Hamiltonian lift + +Given a vector field $X: \mathbb{R}^n \to \mathbb{R}^n$, its **Hamiltonian lift** is the function $H_X: \mathbb{R}^n \times (\mathbb{R}^n)^* \to \mathbb{R}$ defined by + +```math +H_X(x, p) = \langle p, X(x) \rangle = \sum_{i=1}^n p_i X_i(x). +``` + +### From plain Julia functions + +The simplest way to compute a Hamiltonian lift is from a plain Julia function. By default, the function is treated as **autonomous** (time-independent) and **non-variable** (no extra parameter): + +```@example main +# Define a vector field as a Julia function +X(x) = [x[2], -x[1]] + +# Compute its Hamiltonian lift +H = Lift(X) + +# Evaluate at a point (x, p) +x = [1.0, 2.0] +p = [3.0, 4.0] +H(x, p) +``` + +The result is $H(x, p) = p_1 x_2 + p_2 (-x_1) = 3 \times 2 + 4 \times (-1) = 2$. + +### From VectorField type + +You can also use the `OptimalControl.VectorField` type, which allows more control over the function's properties: + +```@example main +# Wrap in VectorField (autonomous, non-variable by default) +X_vf = OptimalControl.VectorField(x -> [x[2], -x[1]]) +H_vf = Lift(X_vf) + +# This returns a HamiltonianLift object +H_vf([1.0, 2.0], [3.0, 4.0]) +``` + +### Non-autonomous case + +For time-dependent vector fields, use `autonomous=false`: + +```@example main +# Non-autonomous vector field: X(t, x) = [t*x[2], -x[1]] +X_na(t, x) = [t * x[2], -x[1]] +H_na = Lift(X_na; autonomous=false) + +# Signature is now H(t, x, p) +H_na(2.0, [1.0, 2.0], [3.0, 4.0]) +``` + +### Variable case + +For vector fields depending on an additional parameter $v$, use `variable=true`: + +```@example main +# Variable vector field: X(x, v) = [x[2] + v, -x[1]] +X_var(x, v) = [x[2] + v, -x[1]] +H_var = Lift(X_var; variable=true) + +# Signature is now H(x, p, v) +H_var([1.0, 2.0], [3.0, 4.0], 1.0) +``` + +## Lie derivative + +The **Lie derivative** of a function $f: \mathbb{R}^n \to \mathbb{R}$ along a vector field $X$ is defined by + +```math +(X \cdot f)(x) = f'(x) \cdot X(x) = \sum_{i=1}^n \frac{\partial f}{\partial x_i}(x) X_i(x). +``` + +This represents the directional derivative of $f$ along $X$. + +### From plain Julia functions + +When using plain Julia functions, they are treated as autonomous and non-variable: + +```@example main +# Vector field and scalar function +φ(x) = [x[2], -x[1]] +f(x) = x[1]^2 + x[2]^2 + +# Lie derivative (using dot operator) +Xf = φ ⋅ f + +# Evaluate at a point +Xf([1.0, 2.0]) +``` + +For the harmonic oscillator with $X(x) = (x_2, -x_1)$ and energy $f(x) = x_1^2 + x_2^2$: + +```math +(X \cdot f)(x) = 2x_1 x_2 + 2x_2(-x_1) = 0, +``` + +which confirms that energy is conserved along trajectories. + +### From VectorField type + +```@example main +# Using VectorField type +X = OptimalControl.VectorField(x -> [x[2], -x[1]]) +g(x) = x[1]^2 + x[2]^2 + +# Lie derivative +Xg = X ⋅ g +Xg([1.0, 2.0]) +``` + +### Alternative syntax + +The `Lie` function is equivalent to the `⋅` operator: + +```@example main +# These are equivalent +result1 = X ⋅ g +result2 = Lie(X, g) + +result1([1.0, 2.0]) == result2([1.0, 2.0]) +``` + +### With keyword arguments + +For non-autonomous or variable cases, use the `Lie` function with keyword arguments: + +```@example main +# Non-autonomous case +φ_na(t, x) = [t + x[2], -x[1]] +f_na(t, x) = t + x[1]^2 + x[2]^2 + +Xf_na = Lie(φ_na, f_na; autonomous=false) +Xf_na(1.0, [1.0, 2.0]) +``` + +```@example main +# Variable case +φ_var(x, v) = [x[2] + v, -x[1]] +f_var(x, v) = x[1]^2 + x[2]^2 + v + +Xf_var = Lie(φ_var, f_var; variable=true) +Xf_var([1.0, 2.0], 1.0) +``` + +## Poisson bracket + +For two functions $f, g: \mathbb{R}^n \times (\mathbb{R}^n)^* \to \mathbb{R}$, the **Poisson bracket** is defined by + +```math +\{f, g\}(x, p) = \sum_{i=1}^n \left( \frac{\partial f}{\partial p_i} \frac{\partial g}{\partial x_i} - \frac{\partial f}{\partial x_i} \frac{\partial g}{\partial p_i} \right). +``` + +### Properties + +The Poisson bracket satisfies: + +- **Bilinearity**: $\{af + bg, h\} = a\{f, h\} + b\{g, h\}$ for scalars $a, b$ +- **Antisymmetry**: $\{f, g\} = -\{g, f\}$ +- **Leibniz rule**: $\{fg, h\} = f\{g, h\} + g\{f, h\}$ +- **Jacobi identity**: $\{\{f, g\}, h\} + \{\{h, f\}, g\} + \{\{g, h\}, f\} = 0$ + +### From plain Julia functions + +```@example main +# Define two Hamiltonian functions +f(x, p) = p[1] * x[2] + p[2] * x[1] +g(x, p) = x[1]^2 + p[2]^2 + +# Compute the Poisson bracket +bracket = Poisson(f, g) + +# Evaluate at a point +x = [1.0, 2.0] +p = [3.0, 4.0] +bracket(x, p) +``` + +### Verify antisymmetry + +```@example main +bracket_fg = Poisson(f, g) +bracket_gf = Poisson(g, f) + +println("Poisson(f, g) = ", bracket_fg(x, p)) +println("Poisson(g, f) = ", bracket_gf(x, p)) +println("Sum = ", bracket_fg(x, p) + bracket_gf(x, p)) +``` + +### From Hamiltonian type + +```@example main +# Wrap in Hamiltonian type +F = OptimalControl.Hamiltonian(f) +G = OptimalControl.Hamiltonian(g) + +bracket_HH = Poisson(F, G) +bracket_HH(x, p) +``` + +### With keyword arguments + +```@example main +# Non-autonomous case +f_na(t, x, p) = t + p[1] * x[2] + p[2] * x[1] +g_na(t, x, p) = t^2 + x[1]^2 + p[2]^2 + +bracket_na = Poisson(f_na, g_na; autonomous=false) +bracket_na(1.0, [1.0, 2.0], [3.0, 4.0]) +``` + +### Relation to Hamiltonian vector fields + +The Poisson bracket is closely related to the Lie derivative. If $\vec{H} = (\nabla_p H, -\nabla_x H)$ denotes the Hamiltonian vector field associated to $H$, then + +```math +\{H, G\} = \vec{H} \cdot G. +``` + +This means the Poisson bracket of $H$ and $G$ equals the Lie derivative of $G$ along the Hamiltonian vector field of $H$. + +### Poisson bracket of Hamiltonian lifts + +When computing the Poisson bracket of two Hamiltonian lifts, the result is the Hamiltonian lift of the Lie bracket of the underlying vector fields: + +```@example main +# Two vector fields +X(x) = [x[1]^2, x[2]^2] +Y(x) = [x[2], -x[1]] + +# Their Hamiltonian lifts +HX = Lift(X) +HY = Lift(Y) + +# Poisson bracket of lifts +bracket_lifts = Poisson(HX, HY) +bracket_lifts([1.0, 2.0], [3.0, 4.0]) +``` + +This satisfies: $\{H_X, H_Y\} = H_{[X,Y]}$ where $[X,Y]$ is the Lie bracket of vector fields (see next section). + +## Lie bracket of vector fields + +For two vector fields $X, Y: \mathbb{R}^n \to \mathbb{R}^n$, the **Lie bracket** is the vector field $[X, Y]$ defined by + +```math +[X, Y](x) = Y'(x) \cdot X(x) - X'(x) \cdot Y(x), +``` + +where $X'(x)$ denotes the Jacobian matrix of $X$ at $x$. + +### From VectorField type + +```@example main +# Define two vector fields +X = OptimalControl.VectorField(x -> [x[2], -x[1]]) +Y = OptimalControl.VectorField(x -> [x[1], x[2]]) + +# Compute the Lie bracket +Z = Lie(X, Y) + +# Evaluate at a point +Z([1.0, 2.0]) +``` + +### Relation to Poisson brackets + +If $H_X = \text{Lift}(X)$ and $H_Y = \text{Lift}(Y)$ are the Hamiltonian lifts, then: + +```math +\{H_X, H_Y\} = H_{[X,Y]}. +``` + +Let's verify this numerically: + +```@example main +# Hamiltonian lifts +HX = Lift(x -> X(x)) +HY = Lift(x -> Y(x)) + +# Poisson bracket of the lifts +bracket_XY = Poisson(HX, HY) + +# Lift of the Lie bracket +HZ = Lift(x -> Z(x)) + +# Compare at a point +x = [1.0, 2.0] +p = [3.0, 4.0] + +println("Poisson bracket: ", bracket_XY(x, p)) +println("Lift of Lie bracket: ", HZ(x, p)) +``` + +## The `@Lie` macro + +The `@Lie` macro provides a convenient syntax for computing Lie brackets (for vector fields) and Poisson brackets (for Hamiltonians). + +### Lie brackets with VectorField + +```@example main +# Define vector fields +F1 = OptimalControl.VectorField(x -> [0, -x[3], x[2]]) +F2 = OptimalControl.VectorField(x -> [x[3], 0, -x[1]]) + +# Compute Lie bracket using macro +L = @Lie [F1, F2] + +# Evaluate +L([1.0, 2.0, 3.0]) +``` + +### Nested Lie brackets + +```@example main +F3 = OptimalControl.VectorField(x -> [x[1], x[2], x[3]]) +nested = @Lie [[F1, F2], F3] +nested([1.0, 2.0, 3.0]) +``` + +### Poisson brackets from plain functions + +For Hamiltonian functions (plain Julia functions), use curly braces `{_, _}`: + +```@example main +# Define Hamiltonian functions +H0(x, p) = p[1] * x[2] + p[2] * (-x[1]) +H1(x, p) = p[2] + +# Compute Poisson bracket +H01 = @Lie {H0, H1} + +# Evaluate +H01([1.0, 2.0], [3.0, 4.0]) +``` + +### Iterated Poisson brackets + +The macro is particularly useful for computing iterated brackets, which appear in singular control analysis: + +```@example main +# First-order bracket +H01 = @Lie {H0, H1} + +# Second-order brackets +H001 = @Lie {H0, H01} +H101 = @Lie {H1, H01} + +# Evaluate +x = [1.0, 2.0] +p = [3.0, 4.0] + +println("H01(x, p) = ", H01(x, p)) +println("H001(x, p) = ", H001(x, p)) +println("H101(x, p) = ", H101(x, p)) +``` + +These iterated brackets are used to compute singular controls. For a pseudo-Hamiltonian of the form $H = H_0 + u H_1$, if the switching function $H_1$ vanishes on an interval (singular arc), the control is given by + +```math +u_s = -\frac{H_{001}}{H_{101}}, +``` + +provided $H_{101} \neq 0$. See the [singular control example](@ref example-singular-control) for a complete application. + +### With keyword arguments + +For non-autonomous functions, specify `autonomous=false`: + +```@example main +# Non-autonomous Hamiltonians +H0_na(t, x, p) = t + p[1] * x[2] + p[2] * (-x[1]) +H1_na(t, x, p) = p[2] + +# Poisson bracket with keyword +H01_na = @Lie {H0_na, H1_na} autonomous=false + +# Evaluate +H01_na(1.0, [1.0, 2.0], [3.0, 4.0]) +``` + +### Poisson brackets from Hamiltonian type + +```@example main +# Using Hamiltonian type +H1_ham = OptimalControl.Hamiltonian((x, p) -> x[1]^2 + p[2]^2) +H2_ham = OptimalControl.Hamiltonian((x, p) -> x[2]^2 + p[1]^2) + +# Macro works with Hamiltonian objects too +P = @Lie {H1_ham, H2_ham} +P([1.0, 1.0], [3.0, 2.0]) +``` + +## Partial time derivative + +For non-autonomous functions $f(t, x, \ldots)$, the **partial derivative with respect to time** is computed using the `∂ₜ` operator: + +```math +(\partial_t f)(t, x, \ldots) = \frac{\partial f}{\partial t}(t, x, \ldots). +``` + +### Basic usage + +```@example main +# Define a time-dependent function +f(t, x) = t * x + +# Compute partial time derivative +df = ∂ₜ(f) + +# Evaluate +df(0, 8) +``` + +```@example main +df(2, 3) +``` + +### More complex example + +```@example main +# Function with multiple arguments +g(t, x, p) = t^2 + x[1] * p[1] + x[2] * p[2] + +# Partial derivative +dg = ∂ₜ(g) + +# At t=3, ∂g/∂t = 2t = 6 +dg(3, [1.0, 2.0], [4.0, 5.0]) +``` + +### Relation to total time derivative + +For a non-autonomous Hamiltonian $H(t, x, p)$ and a function $G(t, x, p)$, the **total time derivative** along the Hamiltonian flow is: + +```math +\frac{d}{dt} G(t, x(t), p(t)) = \partial_t G + \{H, G\}. +``` + +This is the sum of: +- The **partial time derivative** $\partial_t G$ (explicit time dependence) +- The **Poisson bracket** $\{H, G\}$ (evolution along the flow) + +This relation is fundamental in non-autonomous optimal control theory. + +## Summary + +| Function/Operator | Mathematical notation | Julia syntax | +|-------------------|----------------------|--------------| +| Hamiltonian lift | $H_X(x,p) = \langle p, X(x) \rangle$ | `H = Lift(X)` | +| Lie derivative | $(X \cdot f)(x) = f'(x) \cdot X(x)$ | `X ⋅ f` or `Lie(X, f)` | +| Poisson bracket | $\{f,g\}(x,p) = \langle \nabla_p f, \nabla_x g \rangle - \langle \nabla_x f, \nabla_p g \rangle$ | `Poisson(f, g)` or `@Lie {f, g}` | +| Lie bracket | $[X,Y](x) = Y'(x) X(x) - X'(x) Y(x)$ | `Lie(X, Y)` or `@Lie [X, Y]` | +| Partial time derivative | $\partial_t f(t, x, \ldots)$ | `∂ₜ(f)` | + +## See also + +- [Compute flows from Hamiltonians and others](@ref manual-flow-others) — Using flows with Hamiltonian vector fields +- [Singular control example](@ref example-singular-control) — Application to computing singular controls +- [Goddard tutorial](@extref Tutorials tutorial-goddard) — Complex example with bang, singular, and boundary arcs diff --git a/src/imports/ctflows.jl b/src/imports/ctflows.jl index 8ddeedc3..7a61d6e5 100644 --- a/src/imports/ctflows.jl +++ b/src/imports/ctflows.jl @@ -4,7 +4,7 @@ @reexport import CTFlows: CTFlows # for generated code (prefix) # Types -import CTFlows: Hamiltonian, HamiltonianLift, HamiltonianVectorField +import CTFlows: Hamiltonian, HamiltonianLift, HamiltonianVectorField, VectorField # Methods -@reexport import CTFlows: Lift, Flow, ⋅, Lie, Poisson, @Lie, * +@reexport import CTFlows: Lift, Flow, ⋅, Lie, Poisson, @Lie, *, ∂ₜ diff --git a/test/suite/reexport/test_ctflows.jl b/test/suite/reexport/test_ctflows.jl index 3e5fcfbf..f7115414 100644 --- a/test/suite/reexport/test_ctflows.jl +++ b/test/suite/reexport/test_ctflows.jl @@ -23,6 +23,7 @@ function test_ctflows() OptimalControl.Hamiltonian, OptimalControl.HamiltonianLift, OptimalControl.HamiltonianVectorField, + OptimalControl.VectorField, ) Test.@test isdefined(OptimalControl, nameof(T)) Test.@test !isdefined(CurrentModule, nameof(T)) @@ -37,7 +38,7 @@ function test_ctflows() end end Test.@testset "Operators" begin - for op in (:⋅, :Lie, :Poisson, :*) + for op in (:⋅, :Lie, :Poisson, :*, :∂ₜ) Test.@test isdefined(OptimalControl, op) Test.@test isdefined(CurrentModule, op) end @@ -222,6 +223,37 @@ function test_ctflows() result3 = @Lie {H1, H2} Test.@test result3 isa CTFlows.Hamiltonian end + + Test.@testset "VectorField Construction" begin + # Test VectorField construction patterns + X1 = OptimalControl.VectorField(x -> [x[2], -x[1]]) + Test.@test X1 isa OptimalControl.VectorField + Test.@test X1([1, 2]) isa Vector + + # Non-autonomous + X2 = OptimalControl.VectorField((t, x) -> [t + x[2], -x[1]]; autonomous=false) + Test.@test X2 isa OptimalControl.VectorField + Test.@test X2(1.0, [1, 2]) isa Vector + + # Variable + X3 = OptimalControl.VectorField((x, v) -> [x[2] + v, -x[1]]; variable=true) + Test.@test X3 isa OptimalControl.VectorField + Test.@test X3([1, 2], 1.0) isa Vector + end + + Test.@testset "∂ₜ Operator" begin + # Test partial time derivative + f = (t, x) -> t * x + df = ∂ₜ(f) + Test.@test df isa Function + Test.@test df(0, 8) ≈ 8 + Test.@test df(2, 3) ≈ 3 + + # More complex function + g = (t, x, p) -> t^2 + x[1]*p[1] + dg = ∂ₜ(g) + Test.@test dg(3, [1, 2], [4, 5]) ≈ 6 + end end end end From 7da9e59179ad1263d7e6f88c86a94161c7ddc280 Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Thu, 2 Apr 2026 15:13:30 +0200 Subject: [PATCH 04/11] Fix duplicate headings with unique IDs using correct @id syntax --- docs/src/manual-differential-geometry.md | 86 +++++++++++++++--------- 1 file changed, 54 insertions(+), 32 deletions(-) diff --git a/docs/src/manual-differential-geometry.md b/docs/src/manual-differential-geometry.md index e701c636..b4069f0b 100644 --- a/docs/src/manual-differential-geometry.md +++ b/docs/src/manual-differential-geometry.md @@ -1,9 +1,13 @@ # [Differential geometry tools](@id manual-differential-geometry) +```@meta +Draft = false +``` + Optimal control theory relies on differential geometry tools to analyze Hamiltonian systems, compute singular controls, study controllability, and more. This page introduces the main operators available in OptimalControl.jl: Hamiltonian lift, Lie derivatives, Poisson brackets, Lie brackets, and partial time derivatives. !!! note "Type qualification" - + Types like `Hamiltonian`, `HamiltonianLift`, `VectorField`, and `HamiltonianVectorField` are **not exported** by OptimalControl.jl. You must qualify them with `OptimalControl.` when using them (e.g., `OptimalControl.VectorField`). Functions and operators (`Lift`, `⋅`, `Lie`, `Poisson`, `@Lie`, `∂ₜ`) are exported and can be used directly. First, import the package: @@ -43,7 +47,8 @@ The result is $H(x, p) = p_1 x_2 + p_2 (-x_1) = 3 \times 2 + 4 \times (-1) = 2$. You can also use the `OptimalControl.VectorField` type, which allows more control over the function's properties: -```@example main +```@example main-1 +using OptimalControl # hide # Wrap in VectorField (autonomous, non-variable by default) X_vf = OptimalControl.VectorField(x -> [x[2], -x[1]]) H_vf = Lift(X_vf) @@ -56,7 +61,8 @@ H_vf([1.0, 2.0], [3.0, 4.0]) For time-dependent vector fields, use `autonomous=false`: -```@example main +```@example main-2 +using OptimalControl # hide # Non-autonomous vector field: X(t, x) = [t*x[2], -x[1]] X_na(t, x) = [t * x[2], -x[1]] H_na = Lift(X_na; autonomous=false) @@ -69,7 +75,8 @@ H_na(2.0, [1.0, 2.0], [3.0, 4.0]) For vector fields depending on an additional parameter $v$, use `variable=true`: -```@example main +```@example main-3 +using OptimalControl # hide # Variable vector field: X(x, v) = [x[2] + v, -x[1]] X_var(x, v) = [x[2] + v, -x[1]] H_var = Lift(X_var; variable=true) @@ -88,11 +95,12 @@ The **Lie derivative** of a function $f: \mathbb{R}^n \to \mathbb{R}$ along a ve This represents the directional derivative of $f$ along $X$. -### From plain Julia functions +### [From plain Julia functions](@id lie-from-functions) When using plain Julia functions, they are treated as autonomous and non-variable: -```@example main +```@example main-4 +using OptimalControl # hide # Vector field and scalar function φ(x) = [x[2], -x[1]] f(x) = x[1]^2 + x[2]^2 @@ -112,9 +120,10 @@ For the harmonic oscillator with $X(x) = (x_2, -x_1)$ and energy $f(x) = x_1^2 + which confirms that energy is conserved along trajectories. -### From VectorField type +### [From VectorField type](@id lie-from-vectorfield) -```@example main +```@example main-5 +using OptimalControl # hide # Using VectorField type X = OptimalControl.VectorField(x -> [x[2], -x[1]]) g(x) = x[1]^2 + x[2]^2 @@ -128,7 +137,7 @@ Xg([1.0, 2.0]) The `Lie` function is equivalent to the `⋅` operator: -```@example main +```@example main-5 # These are equivalent result1 = X ⋅ g result2 = Lie(X, g) @@ -140,7 +149,8 @@ result1([1.0, 2.0]) == result2([1.0, 2.0]) For non-autonomous or variable cases, use the `Lie` function with keyword arguments: -```@example main +```@example main-6 +using OptimalControl # hide # Non-autonomous case φ_na(t, x) = [t + x[2], -x[1]] f_na(t, x) = t + x[1]^2 + x[2]^2 @@ -149,7 +159,8 @@ Xf_na = Lie(φ_na, f_na; autonomous=false) Xf_na(1.0, [1.0, 2.0]) ``` -```@example main +```@example main-7 +using OptimalControl # hide # Variable case φ_var(x, v) = [x[2] + v, -x[1]] f_var(x, v) = x[1]^2 + x[2]^2 + v @@ -175,9 +186,10 @@ The Poisson bracket satisfies: - **Leibniz rule**: $\{fg, h\} = f\{g, h\} + g\{f, h\}$ - **Jacobi identity**: $\{\{f, g\}, h\} + \{\{h, f\}, g\} + \{\{g, h\}, f\} = 0$ -### From plain Julia functions +### [From plain Julia functions](@id poisson-from-functions) -```@example main +```@example main-8 +using OptimalControl # hide # Define two Hamiltonian functions f(x, p) = p[1] * x[2] + p[2] * x[1] g(x, p) = x[1]^2 + p[2]^2 @@ -193,7 +205,7 @@ bracket(x, p) ### Verify antisymmetry -```@example main +```@example main-8 bracket_fg = Poisson(f, g) bracket_gf = Poisson(g, f) @@ -204,7 +216,7 @@ println("Sum = ", bracket_fg(x, p) + bracket_gf(x, p)) ### From Hamiltonian type -```@example main +```@example main-8 # Wrap in Hamiltonian type F = OptimalControl.Hamiltonian(f) G = OptimalControl.Hamiltonian(g) @@ -213,9 +225,10 @@ bracket_HH = Poisson(F, G) bracket_HH(x, p) ``` -### With keyword arguments +### [With keyword arguments](@id poisson-kwargs) -```@example main +```@example main-9 +using OptimalControl # hide # Non-autonomous case f_na(t, x, p) = t + p[1] * x[2] + p[2] * x[1] g_na(t, x, p) = t^2 + x[1]^2 + p[2]^2 @@ -238,7 +251,8 @@ This means the Poisson bracket of $H$ and $G$ equals the Lie derivative of $G$ a When computing the Poisson bracket of two Hamiltonian lifts, the result is the Hamiltonian lift of the Lie bracket of the underlying vector fields: -```@example main +```@example main-10 +using OptimalControl # hide # Two vector fields X(x) = [x[1]^2, x[2]^2] Y(x) = [x[2], -x[1]] @@ -264,9 +278,10 @@ For two vector fields $X, Y: \mathbb{R}^n \to \mathbb{R}^n$, the **Lie bracket** where $X'(x)$ denotes the Jacobian matrix of $X$ at $x$. -### From VectorField type +### [From VectorField type](@id bracket-from-vectorfield) -```@example main +```@example main-11 +using OptimalControl # hide # Define two vector fields X = OptimalControl.VectorField(x -> [x[2], -x[1]]) Y = OptimalControl.VectorField(x -> [x[1], x[2]]) @@ -288,7 +303,7 @@ If $H_X = \text{Lift}(X)$ and $H_Y = \text{Lift}(Y)$ are the Hamiltonian lifts, Let's verify this numerically: -```@example main +```@example main-11 # Hamiltonian lifts HX = Lift(x -> X(x)) HY = Lift(x -> Y(x)) @@ -313,7 +328,8 @@ The `@Lie` macro provides a convenient syntax for computing Lie brackets (for ve ### Lie brackets with VectorField -```@example main +```@example main-12 +using OptimalControl # hide # Define vector fields F1 = OptimalControl.VectorField(x -> [0, -x[3], x[2]]) F2 = OptimalControl.VectorField(x -> [x[3], 0, -x[1]]) @@ -327,7 +343,7 @@ L([1.0, 2.0, 3.0]) ### Nested Lie brackets -```@example main +```@example main-12 F3 = OptimalControl.VectorField(x -> [x[1], x[2], x[3]]) nested = @Lie [[F1, F2], F3] nested([1.0, 2.0, 3.0]) @@ -337,7 +353,8 @@ nested([1.0, 2.0, 3.0]) For Hamiltonian functions (plain Julia functions), use curly braces `{_, _}`: -```@example main +```@example main-13 +using OptimalControl # hide # Define Hamiltonian functions H0(x, p) = p[1] * x[2] + p[2] * (-x[1]) H1(x, p) = p[2] @@ -353,7 +370,7 @@ H01([1.0, 2.0], [3.0, 4.0]) The macro is particularly useful for computing iterated brackets, which appear in singular control analysis: -```@example main +```@example main-13 # First-order bracket H01 = @Lie {H0, H1} @@ -378,11 +395,12 @@ u_s = -\frac{H_{001}}{H_{101}}, provided $H_{101} \neq 0$. See the [singular control example](@ref example-singular-control) for a complete application. -### With keyword arguments +### [With keyword arguments](@id macro-kwargs) For non-autonomous functions, specify `autonomous=false`: -```@example main +```@example main-14 +using OptimalControl # hide # Non-autonomous Hamiltonians H0_na(t, x, p) = t + p[1] * x[2] + p[2] * (-x[1]) H1_na(t, x, p) = p[2] @@ -396,7 +414,8 @@ H01_na(1.0, [1.0, 2.0], [3.0, 4.0]) ### Poisson brackets from Hamiltonian type -```@example main +```@example main-15 +using OptimalControl # hide # Using Hamiltonian type H1_ham = OptimalControl.Hamiltonian((x, p) -> x[1]^2 + p[2]^2) H2_ham = OptimalControl.Hamiltonian((x, p) -> x[2]^2 + p[1]^2) @@ -416,7 +435,8 @@ For non-autonomous functions $f(t, x, \ldots)$, the **partial derivative with re ### Basic usage -```@example main +```@example main-16 +using OptimalControl # hide # Define a time-dependent function f(t, x) = t * x @@ -427,13 +447,14 @@ df = ∂ₜ(f) df(0, 8) ``` -```@example main +```@example main-16 df(2, 3) ``` ### More complex example -```@example main +```@example main-17 +using OptimalControl # hide # Function with multiple arguments g(t, x, p) = t^2 + x[1] * p[1] + x[2] * p[2] @@ -453,6 +474,7 @@ For a non-autonomous Hamiltonian $H(t, x, p)$ and a function $G(t, x, p)$, the * ``` This is the sum of: + - The **partial time derivative** $\partial_t G$ (explicit time dependence) - The **Poisson bracket** $\{H, G\}$ (evolution along the flow) @@ -461,7 +483,7 @@ This relation is fundamental in non-autonomous optimal control theory. ## Summary | Function/Operator | Mathematical notation | Julia syntax | -|-------------------|----------------------|--------------| +| ----------------- | --------------------- | ------------ | | Hamiltonian lift | $H_X(x,p) = \langle p, X(x) \rangle$ | `H = Lift(X)` | | Lie derivative | $(X \cdot f)(x) = f'(x) \cdot X(x)$ | `X ⋅ f` or `Lie(X, f)` | | Poisson bracket | $\{f,g\}(x,p) = \langle \nabla_p f, \nabla_x g \rangle - \langle \nabla_x f, \nabla_p g \rangle$ | `Poisson(f, g)` or `@Lie {f, g}` | From d12a62394d909f77bb5d422abb937c9b3c16fdba Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Thu, 2 Apr 2026 15:30:05 +0200 Subject: [PATCH 05/11] Add VectorField examples for Lie derivative with keyword arguments --- docs/src/manual-differential-geometry.md | 158 +++++++++++++---------- 1 file changed, 92 insertions(+), 66 deletions(-) diff --git a/docs/src/manual-differential-geometry.md b/docs/src/manual-differential-geometry.md index b4069f0b..9dfc453e 100644 --- a/docs/src/manual-differential-geometry.md +++ b/docs/src/manual-differential-geometry.md @@ -33,12 +33,12 @@ The simplest way to compute a Hamiltonian lift is from a plain Julia function. B X(x) = [x[2], -x[1]] # Compute its Hamiltonian lift -H = Lift(X) +HX = Lift(X) # Evaluate at a point (x, p) -x = [1.0, 2.0] -p = [3.0, 4.0] -H(x, p) +x = [1, 2] +p = [3, 4] +HX(x, p) ``` The result is $H(x, p) = p_1 x_2 + p_2 (-x_1) = 3 \times 2 + 4 \times (-1) = 2$. @@ -50,11 +50,11 @@ You can also use the `OptimalControl.VectorField` type, which allows more contro ```@example main-1 using OptimalControl # hide # Wrap in VectorField (autonomous, non-variable by default) -X_vf = OptimalControl.VectorField(x -> [x[2], -x[1]]) -H_vf = Lift(X_vf) +X = OptimalControl.VectorField(x -> [x[2], -x[1]]) +HX = Lift(X) # This returns a HamiltonianLift object -H_vf([1.0, 2.0], [3.0, 4.0]) +HX([1, 2], [3, 4]) ``` ### Non-autonomous case @@ -64,11 +64,11 @@ For time-dependent vector fields, use `autonomous=false`: ```@example main-2 using OptimalControl # hide # Non-autonomous vector field: X(t, x) = [t*x[2], -x[1]] -X_na(t, x) = [t * x[2], -x[1]] -H_na = Lift(X_na; autonomous=false) +X(t, x) = [t * x[2], -x[1]] +HX = Lift(X; autonomous=false) # Signature is now H(t, x, p) -H_na(2.0, [1.0, 2.0], [3.0, 4.0]) +HX(2, [1, 2], [3, 4]) ``` ### Variable case @@ -78,11 +78,11 @@ For vector fields depending on an additional parameter $v$, use `variable=true`: ```@example main-3 using OptimalControl # hide # Variable vector field: X(x, v) = [x[2] + v, -x[1]] -X_var(x, v) = [x[2] + v, -x[1]] -H_var = Lift(X_var; variable=true) +X(x, v) = [x[2] + v, -x[1]] +HX = Lift(X; variable=true) # Signature is now H(x, p, v) -H_var([1.0, 2.0], [3.0, 4.0], 1.0) +HX([1, 2], [3, 4], 1) ``` ## Lie derivative @@ -102,14 +102,14 @@ When using plain Julia functions, they are treated as autonomous and non-variabl ```@example main-4 using OptimalControl # hide # Vector field and scalar function -φ(x) = [x[2], -x[1]] +X(x) = [x[2], -x[1]] f(x) = x[1]^2 + x[2]^2 # Lie derivative (using dot operator) -Xf = φ ⋅ f +Xf = X ⋅ f # Evaluate at a point -Xf([1.0, 2.0]) +Xf([1, 2]) ``` For the harmonic oscillator with $X(x) = (x_2, -x_1)$ and energy $f(x) = x_1^2 + x_2^2$: @@ -130,7 +130,7 @@ g(x) = x[1]^2 + x[2]^2 # Lie derivative Xg = X ⋅ g -Xg([1.0, 2.0]) +Xg([1, 2]) ``` ### Alternative syntax @@ -139,10 +139,10 @@ The `Lie` function is equivalent to the `⋅` operator: ```@example main-5 # These are equivalent -result1 = X ⋅ g -result2 = Lie(X, g) +Xg1 = X ⋅ g +Xg2 = Lie(X, g) -result1([1.0, 2.0]) == result2([1.0, 2.0]) +Xg1([1, 2]) == Xg2([1, 2]) ``` ### With keyword arguments @@ -152,21 +152,47 @@ For non-autonomous or variable cases, use the `Lie` function with keyword argume ```@example main-6 using OptimalControl # hide # Non-autonomous case -φ_na(t, x) = [t + x[2], -x[1]] -f_na(t, x) = t + x[1]^2 + x[2]^2 +X(t, x) = [t + x[2], -x[1]] +f(t, x) = t + x[1]^2 + x[2]^2 -Xf_na = Lie(φ_na, f_na; autonomous=false) -Xf_na(1.0, [1.0, 2.0]) +Xf = Lie(X, f; autonomous=false) +Xf(1, [1, 2]) ``` ```@example main-7 using OptimalControl # hide # Variable case -φ_var(x, v) = [x[2] + v, -x[1]] -f_var(x, v) = x[1]^2 + x[2]^2 + v +X(x, v) = [x[2] + v, -x[1]] +f(x, v) = x[1]^2 + x[2]^2 + v + +Xf = Lie(X, f; variable=true) +Xf([1, 2], 1) +``` + +### With VectorField type + +You can also create the VectorField explicitly with the keywords, then use it without keywords in the Lie function: + +```@example main-8 +using OptimalControl # hide +# Non-autonomous VectorField created with keywords +X = OptimalControl.VectorField((t, x) -> [t + x[2], -x[1]]; autonomous=false) +f(t, x) = t + x[1]^2 + x[2]^2 + +# No keywords needed here - the VectorField already knows its properties +Xf = Lie(X, f) +Xf(1, [1, 2]) +``` + +```@example main-9 +using OptimalControl # hide +# Variable VectorField created with keywords +X = OptimalControl.VectorField((x, v) -> [x[2] + v, -x[1]]; variable=true) +f(x, v) = x[1]^2 + x[2]^2 + v -Xf_var = Lie(φ_var, f_var; variable=true) -Xf_var([1.0, 2.0], 1.0) +# No keywords needed here +Xf = Lie(X, f) +Xf([1, 2], 1) ``` ## Poisson bracket @@ -195,23 +221,23 @@ f(x, p) = p[1] * x[2] + p[2] * x[1] g(x, p) = x[1]^2 + p[2]^2 # Compute the Poisson bracket -bracket = Poisson(f, g) +Hfg = Poisson(f, g) # Evaluate at a point -x = [1.0, 2.0] -p = [3.0, 4.0] -bracket(x, p) +x = [1, 2] +p = [3, 4] +Hfg(x, p) ``` ### Verify antisymmetry ```@example main-8 -bracket_fg = Poisson(f, g) -bracket_gf = Poisson(g, f) +Hfg = Poisson(f, g) +Hgf = Poisson(g, f) -println("Poisson(f, g) = ", bracket_fg(x, p)) -println("Poisson(g, f) = ", bracket_gf(x, p)) -println("Sum = ", bracket_fg(x, p) + bracket_gf(x, p)) +println("Poisson(f, g) = ", Hfg(x, p)) +println("Poisson(g, f) = ", Hgf(x, p)) +println("Sum = ", Hfg(x, p) + Hgf(x, p)) ``` ### From Hamiltonian type @@ -221,8 +247,8 @@ println("Sum = ", bracket_fg(x, p) + bracket_gf(x, p)) F = OptimalControl.Hamiltonian(f) G = OptimalControl.Hamiltonian(g) -bracket_HH = Poisson(F, G) -bracket_HH(x, p) +Hfg = Poisson(F, G) +Hfg(x, p) ``` ### [With keyword arguments](@id poisson-kwargs) @@ -230,11 +256,11 @@ bracket_HH(x, p) ```@example main-9 using OptimalControl # hide # Non-autonomous case -f_na(t, x, p) = t + p[1] * x[2] + p[2] * x[1] -g_na(t, x, p) = t^2 + x[1]^2 + p[2]^2 +f(t, x, p) = t + p[1] * x[2] + p[2] * x[1] +g(t, x, p) = t^2 + x[1]^2 + p[2]^2 -bracket_na = Poisson(f_na, g_na; autonomous=false) -bracket_na(1.0, [1.0, 2.0], [3.0, 4.0]) +Hfg = Poisson(f, g; autonomous=false) +Hfg(1, [1, 2], [3, 4]) ``` ### Relation to Hamiltonian vector fields @@ -262,8 +288,8 @@ HX = Lift(X) HY = Lift(Y) # Poisson bracket of lifts -bracket_lifts = Poisson(HX, HY) -bracket_lifts([1.0, 2.0], [3.0, 4.0]) +HXY = Poisson(HX, HY) +HXY([1, 2], [3, 4]) ``` This satisfies: $\{H_X, H_Y\} = H_{[X,Y]}$ where $[X,Y]$ is the Lie bracket of vector fields (see next section). @@ -290,7 +316,7 @@ Y = OptimalControl.VectorField(x -> [x[1], x[2]]) Z = Lie(X, Y) # Evaluate at a point -Z([1.0, 2.0]) +Z([1, 2]) ``` ### Relation to Poisson brackets @@ -309,16 +335,16 @@ HX = Lift(x -> X(x)) HY = Lift(x -> Y(x)) # Poisson bracket of the lifts -bracket_XY = Poisson(HX, HY) +HXY = Poisson(HX, HY) # Lift of the Lie bracket HZ = Lift(x -> Z(x)) # Compare at a point -x = [1.0, 2.0] -p = [3.0, 4.0] +x = [1, 2] +p = [3, 4] -println("Poisson bracket: ", bracket_XY(x, p)) +println("Poisson bracket: ", HXY(x, p)) println("Lift of Lie bracket: ", HZ(x, p)) ``` @@ -335,18 +361,18 @@ F1 = OptimalControl.VectorField(x -> [0, -x[3], x[2]]) F2 = OptimalControl.VectorField(x -> [x[3], 0, -x[1]]) # Compute Lie bracket using macro -L = @Lie [F1, F2] +F12 = @Lie [F1, F2] # Evaluate -L([1.0, 2.0, 3.0]) +F12([1, 2, 3]) ``` ### Nested Lie brackets ```@example main-12 F3 = OptimalControl.VectorField(x -> [x[1], x[2], x[3]]) -nested = @Lie [[F1, F2], F3] -nested([1.0, 2.0, 3.0]) +F123 = @Lie [[F1, F2], F3] +F123([1, 2, 3]) ``` ### Poisson brackets from plain functions @@ -363,7 +389,7 @@ H1(x, p) = p[2] H01 = @Lie {H0, H1} # Evaluate -H01([1.0, 2.0], [3.0, 4.0]) +H01([1, 2], [3, 4]) ``` ### Iterated Poisson brackets @@ -379,8 +405,8 @@ H001 = @Lie {H0, H01} H101 = @Lie {H1, H01} # Evaluate -x = [1.0, 2.0] -p = [3.0, 4.0] +x = [1, 2] +p = [3, 4] println("H01(x, p) = ", H01(x, p)) println("H001(x, p) = ", H001(x, p)) @@ -402,14 +428,14 @@ For non-autonomous functions, specify `autonomous=false`: ```@example main-14 using OptimalControl # hide # Non-autonomous Hamiltonians -H0_na(t, x, p) = t + p[1] * x[2] + p[2] * (-x[1]) -H1_na(t, x, p) = p[2] +H0(t, x, p) = t + p[1] * x[2] + p[2] * (-x[1]) +H1(t, x, p) = p[2] # Poisson bracket with keyword -H01_na = @Lie {H0_na, H1_na} autonomous=false +H01 = @Lie {H0, H1} autonomous=false # Evaluate -H01_na(1.0, [1.0, 2.0], [3.0, 4.0]) +H01(1, [1, 2], [3, 4]) ``` ### Poisson brackets from Hamiltonian type @@ -417,12 +443,12 @@ H01_na(1.0, [1.0, 2.0], [3.0, 4.0]) ```@example main-15 using OptimalControl # hide # Using Hamiltonian type -H1_ham = OptimalControl.Hamiltonian((x, p) -> x[1]^2 + p[2]^2) -H2_ham = OptimalControl.Hamiltonian((x, p) -> x[2]^2 + p[1]^2) +H1 = OptimalControl.Hamiltonian((x, p) -> x[1]^2 + p[2]^2) +H2 = OptimalControl.Hamiltonian((x, p) -> x[2]^2 + p[1]^2) # Macro works with Hamiltonian objects too -P = @Lie {H1_ham, H2_ham} -P([1.0, 1.0], [3.0, 2.0]) +H12 = @Lie {H1, H2} +H12([1, 1], [3, 2]) ``` ## Partial time derivative @@ -462,7 +488,7 @@ g(t, x, p) = t^2 + x[1] * p[1] + x[2] * p[2] dg = ∂ₜ(g) # At t=3, ∂g/∂t = 2t = 6 -dg(3, [1.0, 2.0], [4.0, 5.0]) +dg(3, [1, 2], [4, 5]) ``` ### Relation to total time derivative From e011b1d73d92c77a0f7bde4221fb4e72f074d67a Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Thu, 2 Apr 2026 15:34:34 +0200 Subject: [PATCH 06/11] Add Hamiltonian examples with keywords to Poisson bracket section - Show how to create Hamiltonian objects with autonomous/variable keywords - Explain that both Hamiltonians must have same dependencies - Add non-autonomous and variable examples --- docs/src/manual-differential-geometry.md | 32 ++++++++++++++++++++++++ 1 file changed, 32 insertions(+) diff --git a/docs/src/manual-differential-geometry.md b/docs/src/manual-differential-geometry.md index 9dfc453e..bce8a8b4 100644 --- a/docs/src/manual-differential-geometry.md +++ b/docs/src/manual-differential-geometry.md @@ -263,6 +263,38 @@ Hfg = Poisson(f, g; autonomous=false) Hfg(1, [1, 2], [3, 4]) ``` +### With Hamiltonian type and keywords + +You can also create Hamiltonian objects explicitly with keywords, then use them without keywords in the Poisson function. **Important**: both Hamiltonians must have the same time and variable dependencies: + +```@example main-10 +using OptimalControl # hide +# Non-autonomous Hamiltonians created with keywords +f_na(t, x, p) = t + p[1] * x[2] + p[2] * x[1] +g_na(t, x, p) = t^2 + x[1]^2 + p[2]^2 + +F = OptimalControl.Hamiltonian(f_na; autonomous=false) +G = OptimalControl.Hamiltonian(g_na; autonomous=false) + +# No keywords needed here - both Hamiltonians are already non-autonomous +Hfg = Poisson(F, G) +Hfg(1, [1, 2], [3, 4]) +``` + +```@example main-11 +using OptimalControl # hide +# Variable Hamiltonians created with keywords +f_var(x, p, v) = x[1]^2 + p[2]^2 + v +g_var(x, p, v) = x[2]^2 + p[1]^2 + 2*v + +F = OptimalControl.Hamiltonian(f_var; variable=true) +G = OptimalControl.Hamiltonian(g_var; variable=true) + +# Both are variable, so the Poisson bracket is also variable +Hfg = Poisson(F, G) +Hfg([1, 2], [3, 4], 1) +``` + ### Relation to Hamiltonian vector fields The Poisson bracket is closely related to the Lie derivative. If $\vec{H} = (\nabla_p H, -\nabla_x H)$ denotes the Hamiltonian vector field associated to $H$, then From c010f47872b2adc4bc442c56b11e5845c5771d6d Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Thu, 2 Apr 2026 23:33:20 +0200 Subject: [PATCH 07/11] Add support for plain functions in @Lie macro for Lie brackets MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit - Update documentation warning to reflect new CTFlows capability - Add comprehensive examples with plain functions (autonomous, non-autonomous, variable) - Add nested brackets and mixed VectorField/function examples - Add tip comparing plain functions vs explicit VectorField creation - Add extensive test suite for @Lie macro with plain functions - All tests pass (89/89) ✅ --- docs/src/manual-differential-geometry.md | 107 ++++++++++++++++++++--- test/suite/reexport/test_ctflows.jl | 104 +++++++++++++++++++++- 2 files changed, 198 insertions(+), 13 deletions(-) diff --git a/docs/src/manual-differential-geometry.md b/docs/src/manual-differential-geometry.md index bce8a8b4..57a2ef3d 100644 --- a/docs/src/manual-differential-geometry.md +++ b/docs/src/manual-differential-geometry.md @@ -173,7 +173,7 @@ Xf([1, 2], 1) You can also create the VectorField explicitly with the keywords, then use it without keywords in the Lie function: -```@example main-8 +```@example main-7a using OptimalControl # hide # Non-autonomous VectorField created with keywords X = OptimalControl.VectorField((t, x) -> [t + x[2], -x[1]]; autonomous=false) @@ -184,7 +184,7 @@ Xf = Lie(X, f) Xf(1, [1, 2]) ``` -```@example main-9 +```@example main-7b using OptimalControl # hide # Variable VectorField created with keywords X = OptimalControl.VectorField((x, v) -> [x[2] + v, -x[1]]; variable=true) @@ -267,28 +267,28 @@ Hfg(1, [1, 2], [3, 4]) You can also create Hamiltonian objects explicitly with keywords, then use them without keywords in the Poisson function. **Important**: both Hamiltonians must have the same time and variable dependencies: -```@example main-10 +```@example main-9a using OptimalControl # hide # Non-autonomous Hamiltonians created with keywords -f_na(t, x, p) = t + p[1] * x[2] + p[2] * x[1] -g_na(t, x, p) = t^2 + x[1]^2 + p[2]^2 +f(t, x, p) = t + p[1] * x[2] + p[2] * x[1] +g(t, x, p) = t^2 + x[1]^2 + p[2]^2 -F = OptimalControl.Hamiltonian(f_na; autonomous=false) -G = OptimalControl.Hamiltonian(g_na; autonomous=false) +F = OptimalControl.Hamiltonian(f; autonomous=false) +G = OptimalControl.Hamiltonian(g; autonomous=false) # No keywords needed here - both Hamiltonians are already non-autonomous Hfg = Poisson(F, G) Hfg(1, [1, 2], [3, 4]) ``` -```@example main-11 +```@example main-9b using OptimalControl # hide # Variable Hamiltonians created with keywords -f_var(x, p, v) = x[1]^2 + p[2]^2 + v -g_var(x, p, v) = x[2]^2 + p[1]^2 + 2*v +f(x, p, v) = x[1]^2 + p[2]^2 + v +g(x, p, v) = x[2]^2 + p[1]^2 + 2*v -F = OptimalControl.Hamiltonian(f_var; variable=true) -G = OptimalControl.Hamiltonian(g_var; variable=true) +F = OptimalControl.Hamiltonian(f; variable=true) +G = OptimalControl.Hamiltonian(g; variable=true) # Both are variable, so the Poisson bracket is also variable Hfg = Poisson(F, G) @@ -384,6 +384,17 @@ println("Lift of Lie bracket: ", HZ(x, p)) The `@Lie` macro provides a convenient syntax for computing Lie brackets (for vector fields) and Poisson brackets (for Hamiltonians). +!!! warning "Important distinction" + +- **Square brackets `[...]`** denote **Lie brackets** and work with: + - `VectorField` objects + - Plain Julia functions (automatically wrapped as `VectorField`) +- **Curly braces `{...}`** denote **Poisson brackets** and work with: + - Plain Julia functions (automatically wrapped as `Hamiltonian`) + - `Hamiltonian` objects + +When using plain functions, specify `autonomous` and `variable` keywords as needed to match your function signature. + ### Lie brackets with VectorField ```@example main-12 @@ -407,6 +418,78 @@ F123 = @Lie [[F1, F2], F3] F123([1, 2, 3]) ``` +### Lie brackets with plain Julia functions + +You can also use plain Julia functions directly with the `@Lie` macro. The functions will be automatically wrapped in `VectorField` objects: + +```@example main-12a +using OptimalControl # hide +# Define plain Julia functions +X(x) = [x[2], -x[1]] +Y(x) = [x[1], x[2]] + +# Compute Lie bracket using macro with plain functions +Z = @Lie [X, Y] + +# Evaluate +Z([1, 2]) +``` + +### With keyword arguments for plain functions + +For non-autonomous or variable cases, specify the keywords: + +```@example main-12b +using OptimalControl # hide +# Non-autonomous plain functions +X(t, x) = [t + x[2], -x[1]] +Y(t, x) = [x[1], t*x[2]] + +# Use autonomous=false keyword +Z = @Lie [X, Y] autonomous=false +Z(1, [1, 2]) +``` + +```@example main-12c +using OptimalControl # hide +# Variable plain functions +X(x, v) = [x[2] + v, -x[1]] +Y(x, v) = [x[1], x[2] + v] + +# Use variable=true keyword +Z = @Lie [X, Y] variable=true +Z([1, 2], 1) +``` + +### Nested brackets with plain functions + +```@example main-12d +using OptimalControl # hide +X(x) = [0, -x[3], x[2]] +Y(x) = [x[3], 0, -x[1]] +Z_func(x) = [x[1], x[2], x[3]] + +# Nested Lie brackets +nested = @Lie [[X, Y], Z_func] +nested([1, 2, 3]) +``` + +!!! tip "Plain functions vs VectorField" + +Using plain functions with `@Lie [X, Y]` is convenient for quick computations. However, if you need to reuse the same vector field multiple times or want explicit control over the autonomy/variability, consider creating `VectorField` objects explicitly: + +```julia +# Explicit VectorField (keywords at creation) +X = OptimalControl.VectorField((t, x) -> [t + x[2], -x[1]]; autonomous=false) +Y = OptimalControl.VectorField((t, x) -> [x[1], t*x[2]]; autonomous=false) +Z = @Lie [X, Y] # No keywords needed + +# Plain functions (keywords at macro call) +X_func(t, x) = [t + x[2], -x[1]] +Y_func(t, x) = [x[1], t*x[2]] +Z = @Lie [X_func, Y_func] autonomous=false +``` + ### Poisson brackets from plain functions For Hamiltonian functions (plain Julia functions), use curly braces `{_, _}`: diff --git a/test/suite/reexport/test_ctflows.jl b/test/suite/reexport/test_ctflows.jl index f7115414..66ca73f3 100644 --- a/test/suite/reexport/test_ctflows.jl +++ b/test/suite/reexport/test_ctflows.jl @@ -129,7 +129,7 @@ function test_ctflows() end Test.@testset "@Lie Macro" begin - # Test basic macro usage + # Test basic macro usage with VectorField X1 = CTFlows.VectorField(x -> [x[2], -x[1]]) X2 = CTFlows.VectorField(x -> [x[1], x[2]]) @@ -141,6 +141,108 @@ function test_ctflows() Test.@test lie_macro_result([1, 2]) isa Vector end + Test.@testset "@Lie Macro with Plain Functions" begin + # ================================================================ + # Autonomous plain functions + # ================================================================ + Test.@testset "Autonomous plain functions" begin + X(x) = [x[2], -x[1]] + Y(x) = [x[1], x[2]] + + # Lie bracket with macro + Z = @Lie [X, Y] + Test.@test Z isa CTFlows.VectorField + Test.@test Z([1, 2]) isa Vector + + # Should give same result as with VectorField objects + X_vf = CTFlows.VectorField(X) + Y_vf = CTFlows.VectorField(Y) + Z_vf = @Lie [X_vf, Y_vf] + Test.@test Z([1, 2]) ≈ Z_vf([1, 2]) + end + + # ================================================================ + # Non-autonomous plain functions + # ================================================================ + Test.@testset "Non-autonomous plain functions" begin + X(t, x) = [t + x[2], -x[1]] + Y(t, x) = [x[1], t * x[2]] + + Z = @Lie [X, Y] autonomous = false + Test.@test Z isa CTFlows.VectorField + Test.@test Z(1, [1, 2]) isa Vector + + # Verify against VectorField version + X_vf = CTFlows.VectorField(X; autonomous=false) + Y_vf = CTFlows.VectorField(Y; autonomous=false) + Z_vf = @Lie [X_vf, Y_vf] + Test.@test Z(1, [1, 2]) ≈ Z_vf(1, [1, 2]) + end + + # ================================================================ + # Variable plain functions + # ================================================================ + Test.@testset "Variable plain functions" begin + X(x, v) = [x[2] + v, -x[1]] + Y(x, v) = [x[1], x[2] + v] + + Z = @Lie [X, Y] variable = true + Test.@test Z isa CTFlows.VectorField + Test.@test Z([1, 2], 1) isa Vector + + # Verify against VectorField version + X_vf = CTFlows.VectorField(X; variable=true) + Y_vf = CTFlows.VectorField(Y; variable=true) + Z_vf = @Lie [X_vf, Y_vf] + Test.@test Z([1, 2], 1) ≈ Z_vf([1, 2], 1) + end + + # ================================================================ + # Non-autonomous + variable plain functions + # ================================================================ + Test.@testset "Non-autonomous variable plain functions" begin + X(t, x, v) = [t + x[2] + v, -x[1]] + Y(t, x, v) = [x[1], t * x[2] + v] + + Z = @Lie [X, Y] autonomous = false variable = true + Test.@test Z isa CTFlows.VectorField + Test.@test Z(1, [1, 2], 1) isa Vector + + # Verify against VectorField version + X_vf = CTFlows.VectorField(X; autonomous=false, variable=true) + Y_vf = CTFlows.VectorField(Y; autonomous=false, variable=true) + Z_vf = @Lie [X_vf, Y_vf] + Test.@test Z(1, [1, 2], 1) ≈ Z_vf(1, [1, 2], 1) + end + + # ================================================================ + # Nested Lie brackets with plain functions + # ================================================================ + Test.@testset "Nested brackets with plain functions" begin + X(x) = [x[2], -x[1]] + Y(x) = [x[1], x[2]] + Z_func(x) = [0, x[1]] + + # [[X, Y], Z] + nested = @Lie [[X, Y], Z_func] + Test.@test nested isa CTFlows.VectorField + Test.@test nested([1, 2]) isa Vector + end + + # ================================================================ + # Mixed: plain function + VectorField + # ================================================================ + Test.@testset "Mixed plain function and VectorField" begin + X(x) = [x[2], -x[1]] + Y_vf = CTFlows.VectorField(x -> [x[1], x[2]]) + + # Should work with one plain function and one VectorField + Z = @Lie [X, Y_vf] + Test.@test Z isa CTFlows.VectorField + Test.@test Z([1, 2]) isa Vector + end + end + Test.@testset "Complex Signature Tests" begin # Test with different arities and keyword arguments From 60eca3a61beb4d93bd01a51897ae9197967db585 Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Thu, 2 Apr 2026 23:34:16 +0200 Subject: [PATCH 08/11] Clarify when keywords are needed for @Lie macro - Specify that keywords are only needed when using only plain functions - When mixing with VectorField objects, keywords are inferred from VectorField - Removes ambiguity about when to specify autonomous/variable keywords --- docs/src/manual-differential-geometry.md | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/docs/src/manual-differential-geometry.md b/docs/src/manual-differential-geometry.md index 57a2ef3d..853c7dff 100644 --- a/docs/src/manual-differential-geometry.md +++ b/docs/src/manual-differential-geometry.md @@ -33,12 +33,12 @@ The simplest way to compute a Hamiltonian lift is from a plain Julia function. B X(x) = [x[2], -x[1]] # Compute its Hamiltonian lift -HX = Lift(X) +H = Lift(X) # Evaluate at a point (x, p) x = [1, 2] p = [3, 4] -HX(x, p) +H(x, p) ``` The result is $H(x, p) = p_1 x_2 + p_2 (-x_1) = 3 \times 2 + 4 \times (-1) = 2$. @@ -51,10 +51,10 @@ You can also use the `OptimalControl.VectorField` type, which allows more contro using OptimalControl # hide # Wrap in VectorField (autonomous, non-variable by default) X = OptimalControl.VectorField(x -> [x[2], -x[1]]) -HX = Lift(X) +H = Lift(X) # This returns a HamiltonianLift object -HX([1, 2], [3, 4]) +H([1, 2], [3, 4]) ``` ### Non-autonomous case @@ -65,10 +65,10 @@ For time-dependent vector fields, use `autonomous=false`: using OptimalControl # hide # Non-autonomous vector field: X(t, x) = [t*x[2], -x[1]] X(t, x) = [t * x[2], -x[1]] -HX = Lift(X; autonomous=false) +H = Lift(X; autonomous=false) # Signature is now H(t, x, p) -HX(2, [1, 2], [3, 4]) +H(2, [1, 2], [3, 4]) ``` ### Variable case @@ -79,10 +79,10 @@ For vector fields depending on an additional parameter $v$, use `variable=true`: using OptimalControl # hide # Variable vector field: X(x, v) = [x[2] + v, -x[1]] X(x, v) = [x[2] + v, -x[1]] -HX = Lift(X; variable=true) +H = Lift(X; variable=true) # Signature is now H(x, p, v) -HX([1, 2], [3, 4], 1) +H([1, 2], [3, 4], 1) ``` ## Lie derivative @@ -393,7 +393,7 @@ The `@Lie` macro provides a convenient syntax for computing Lie brackets (for ve - Plain Julia functions (automatically wrapped as `Hamiltonian`) - `Hamiltonian` objects -When using plain functions, specify `autonomous` and `variable` keywords as needed to match your function signature. +When using **only plain functions** (no VectorField objects), specify `autonomous` and `variable` keywords as needed to match your function signature. If you mix plain functions with VectorField objects, the keywords are inferred from the VectorField objects. ### Lie brackets with VectorField From b70eae74f549240ad4573c50408ed35b4b75a8cb Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Thu, 2 Apr 2026 23:35:51 +0200 Subject: [PATCH 09/11] Further clarify keyword usage for @Lie macro - Keywords are optional when using plain functions - Default values: autonomous=true, variable=false - Can specify only one keyword if needed - Clearer explanation of when keywords are required vs optional --- docs/src/manual-differential-geometry.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/src/manual-differential-geometry.md b/docs/src/manual-differential-geometry.md index 853c7dff..bb102be5 100644 --- a/docs/src/manual-differential-geometry.md +++ b/docs/src/manual-differential-geometry.md @@ -393,7 +393,7 @@ The `@Lie` macro provides a convenient syntax for computing Lie brackets (for ve - Plain Julia functions (automatically wrapped as `Hamiltonian`) - `Hamiltonian` objects -When using **only plain functions** (no VectorField objects), specify `autonomous` and `variable` keywords as needed to match your function signature. If you mix plain functions with VectorField objects, the keywords are inferred from the VectorField objects. +When using **only plain functions** (no `VectorField` or `Hamiltonian` objects), specify `autonomous` and/or `variable` keywords as needed to match your function signature. Keywords are optional - if not specified, they use the default values (`autonomous=true`, `variable=false`). If you mix plain functions with `VectorField` or `Hamiltonian` objects, the keywords are inferred from the `VectorField` or `Hamiltonian` objects. ### Lie brackets with VectorField From acbd1a517714a62f752aac20bf769b4203038637 Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Thu, 2 Apr 2026 23:46:25 +0200 Subject: [PATCH 10/11] Finalize differential geometry documentation improvements MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit - Clarify keyword usage for @Lie macro (optional, defaults, single keyword) - Improve formatting of warning box with proper indentation - Standardize variable naming in examples (Hfg -> H, Z_func -> Z) - Update tip section with consistent naming and formatting - Documentation builds successfully ✅ --- docs/src/assets/Manifest.toml | 337 ++++++++++++----------- docs/src/manual-differential-geometry.md | 68 +++-- 2 files changed, 203 insertions(+), 202 deletions(-) diff --git a/docs/src/assets/Manifest.toml b/docs/src/assets/Manifest.toml index 64f46c30..2140cea3 100644 --- a/docs/src/assets/Manifest.toml +++ b/docs/src/assets/Manifest.toml @@ -1,6 +1,6 @@ # This file is machine-generated - editing it directly is not advised -julia_version = "1.12.1" +julia_version = "1.12.5" manifest_format = "2.0" project_hash = "d470f84ad521e691a87a863486162d9840a77916" @@ -56,9 +56,9 @@ version = "0.4.5" [[deps.Accessors]] deps = ["CompositionsBase", "ConstructionBase", "Dates", "InverseFunctions", "MacroTools"] -git-tree-sha1 = "856ecd7cebb68e5fc87abecd2326ad59f0f911f3" +git-tree-sha1 = "2eeb2c9bef11013efc6f8f97f32ee59b146b09fb" uuid = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697" -version = "0.1.43" +version = "0.1.44" [deps.Accessors.extensions] AxisKeysExt = "AxisKeys" @@ -141,9 +141,9 @@ version = "1.11.0" [[deps.Atomix]] deps = ["UnsafeAtomics"] -git-tree-sha1 = "29bb0eb6f578a587a49da16564705968667f5fa8" +git-tree-sha1 = "b8651b2eb5796a386b0398a20b519a6a6150f75c" uuid = "a9b6321e-bd34-4604-b9c9-b65b8de01458" -version = "1.1.2" +version = "1.1.3" [deps.Atomix.extensions] AtomixCUDAExt = "CUDA" @@ -180,9 +180,9 @@ version = "0.1.6" [[deps.BracketingNonlinearSolve]] deps = ["CommonSolve", "ConcreteStructs", "NonlinearSolveBase", "PrecompileTools", "Reexport", "SciMLBase"] -git-tree-sha1 = "4999dff8efd76814f6662519b985aeda975a1924" +git-tree-sha1 = "d9b66401c1fa982c7ca984d0566af5a9b3551420" uuid = "70df07ce-3d50-431d-a3e7-ca6ddb60ac1e" -version = "1.11.0" +version = "1.12.0" weakdeps = ["ChainRulesCore", "ForwardDiff"] [deps.BracketingNonlinearSolve.extensions] @@ -208,9 +208,9 @@ version = "0.2.7" [[deps.CTBase]] deps = ["DocStringExtensions"] -git-tree-sha1 = "fac598a2d962f564824d37494a307652941c723d" +git-tree-sha1 = "2f689cdb1c28d452f143f2c76897cd5273e89cf7" uuid = "54762871-cc72-4466-b8e8-f6c8b58076cd" -version = "0.18.6-beta" +version = "0.18.7" [deps.CTBase.extensions] CoveragePostprocessing = ["Coverage"] @@ -225,16 +225,16 @@ version = "0.18.6-beta" Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [[deps.CTDirect]] -deps = ["ADNLPModels", "CTModels", "CTSolvers", "DocStringExtensions", "ExaModels", "SolverCore", "SparseArrays"] -git-tree-sha1 = "9d9c1c5c1d17cc02692378ae49d03e90b0e469e8" +deps = ["ADNLPModels", "CTModels", "CTSolvers", "DocStringExtensions", "ExaModels", "SolverCore", "SparseArrays", "SparseConnectivityTracer"] +git-tree-sha1 = "db1699ffab2f31aeda5dbb61dfa9015773cb70fc" uuid = "790bbbee-bee9-49ee-8912-a9de031322d5" -version = "1.0.5" +version = "1.0.6" [[deps.CTFlows]] deps = ["CTBase", "CTModels", "DocStringExtensions", "ForwardDiff", "LinearAlgebra", "MLStyle", "MacroTools"] -git-tree-sha1 = "71ec5ebc9464b1d79e64ea2e53675fa0506e20c6" +git-tree-sha1 = "d89a9defa5901dd1d745042c8e1ea5af87977104" uuid = "1c39547c-7794-42f7-af83-d98194f657c2" -version = "0.8.16-beta" +version = "0.8.19-beta" weakdeps = ["OrdinaryDiffEq"] [deps.CTFlows.extensions] @@ -242,9 +242,9 @@ weakdeps = ["OrdinaryDiffEq"] [[deps.CTModels]] deps = ["CTBase", "DocStringExtensions", "LinearAlgebra", "MLStyle", "MacroTools", "OrderedCollections", "Parameters", "RecipesBase"] -git-tree-sha1 = "c90116a8e74243ae258329325f0b7545cc5385f5" +git-tree-sha1 = "c878ed38da4040f618a459c30cec8e53286ddc26" uuid = "34c4fa32-2049-4079-8329-de33c2a22e2d" -version = "0.9.10-beta" +version = "0.9.11" weakdeps = ["JLD2", "JSON3", "Plots"] [deps.CTModels.extensions] @@ -260,9 +260,9 @@ version = "0.8.10-beta" [[deps.CTSolvers]] deps = ["ADNLPModels", "CTBase", "CTModels", "CommonSolve", "DocStringExtensions", "ExaModels", "KernelAbstractions", "NLPModels", "SolverCore"] -git-tree-sha1 = "21092a83de84623f3d2e55b301ffa54d8cb10e3b" +git-tree-sha1 = "46f28bf27a6158333527417d97787b8125b1a07c" uuid = "d3e8d392-8e4b-4d9b-8e92-d7d4e3650ef6" -version = "0.4.10-beta" +version = "0.4.12" [deps.CTSolvers.extensions] CTSolversCUDA = "CUDA" @@ -341,16 +341,16 @@ uuid = "4889d778-9329-5762-9fec-0578a5d30366" version = "0.7.1+0" [[deps.Cairo_jll]] -deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"] -git-tree-sha1 = "a21c5464519504e41e0cbc91f0188e8ca23d7440" +deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "Libdl", "Pixman_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"] +git-tree-sha1 = "d0efe2c6fdcdaa1c161d206aa8b933788397ec71" uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a" -version = "1.18.5+1" +version = "1.18.6+0" [[deps.ChainRulesCore]] deps = ["Compat", "LinearAlgebra"] -git-tree-sha1 = "e4c6a16e77171a5f5e25e9646617ab1c276c5607" +git-tree-sha1 = "12177ad6b3cad7fd50c8b3825ce24a99ad61c18f" uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" -version = "1.26.0" +version = "1.26.1" weakdeps = ["SparseArrays"] [deps.ChainRulesCore.extensions] @@ -512,9 +512,9 @@ version = "1.8.1" [[deps.DataStructures]] deps = ["OrderedCollections"] -git-tree-sha1 = "e357641bb3e0638d353c4b29ea0e40ea644066a6" +git-tree-sha1 = "e86f4a2805f7f19bec5129bc9150c38208e5dc23" uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8" -version = "0.19.3" +version = "0.19.4" [[deps.DataValueInterfaces]] git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6" @@ -540,13 +540,14 @@ version = "1.9.1" [[deps.DiffEqBase]] deps = ["ArrayInterface", "BracketingNonlinearSolve", "ConcreteStructs", "DocStringExtensions", "FastBroadcast", "FastClosures", "FastPower", "FunctionWrappers", "FunctionWrappersWrappers", "LinearAlgebra", "Logging", "Markdown", "MuladdMacro", "PrecompileTools", "Printf", "RecursiveArrayTools", "Reexport", "SciMLBase", "SciMLOperators", "SciMLStructures", "Setfield", "Static", "StaticArraysCore", "SymbolicIndexingInterface", "TruncatedStacktraces"] -git-tree-sha1 = "1719cd1b0a12e01775dc6db1577dd6ace1798fee" +git-tree-sha1 = "803d463050fae6121f5d15fd449e9538cb993ad9" uuid = "2b5f629d-d688-5b77-993f-72d75c75574e" -version = "6.210.1" +version = "6.214.1" [deps.DiffEqBase.extensions] DiffEqBaseCUDAExt = "CUDA" DiffEqBaseChainRulesCoreExt = "ChainRulesCore" + DiffEqBaseDynamicQuantitiesExt = "DynamicQuantities" DiffEqBaseEnzymeExt = ["ChainRulesCore", "Enzyme"] DiffEqBaseFlexUnitsExt = "FlexUnits" DiffEqBaseForwardDiffExt = ["ForwardDiff"] @@ -565,6 +566,7 @@ version = "6.210.1" CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba" ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f" + DynamicQuantities = "06fc5a27-2a28-4c7c-a15d-362465fb6821" Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9" FlexUnits = "76e01b6b-c995-4ce6-8559-91e72a3d4e95" ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210" @@ -678,7 +680,7 @@ version = "0.2.0" [[deps.Downloads]] deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"] uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6" -version = "1.6.0" +version = "1.7.0" [[deps.EnumX]] git-tree-sha1 = "c49898e8438c828577f04b92fc9368c388ac783c" @@ -686,9 +688,9 @@ uuid = "4e289a0a-7415-4d19-859d-a7e5c4648b56" version = "1.0.7" [[deps.EnzymeCore]] -git-tree-sha1 = "990991b8aa76d17693a98e3a915ac7aa49f08d1a" +git-tree-sha1 = "24bbb6fc8fb87eb71c1f8d00184a60fc22c63903" uuid = "f151be2c-9106-41f4-ab19-57ee4f262869" -version = "0.8.18" +version = "0.8.19" weakdeps = ["Adapt", "ChainRulesCore"] [deps.EnzymeCore.extensions] @@ -779,10 +781,15 @@ uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5" version = "8.0.1+1" [[deps.FastBroadcast]] -deps = ["ArrayInterface", "LinearAlgebra", "Polyester", "Static", "StaticArrayInterface", "StrideArraysCore"] -git-tree-sha1 = "ab1b34570bcdf272899062e1a56285a53ecaae08" +deps = ["ArrayInterface", "LinearAlgebra"] +git-tree-sha1 = "e3e64918b1604ba8b1734c4a27febdfe5d09e235" uuid = "7034ab61-46d4-4ed7-9d0f-46aef9175898" -version = "0.3.5" +version = "1.3.1" +weakdeps = ["Polyester", "Static"] + + [deps.FastBroadcast.extensions] + FastBroadcastPolyesterExt = "Polyester" + FastBroadcastStaticExt = "Static" [[deps.FastClosures]] git-tree-sha1 = "acebe244d53ee1b461970f8910c235b259e772ef" @@ -887,9 +894,9 @@ version = "1.3.7" [[deps.ForwardDiff]] deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions"] -git-tree-sha1 = "eef4c86803f47dcb61e9b8790ecaa96956fdd8ae" +git-tree-sha1 = "cddeab6487248a39dae1a960fff0ac17b2a28888" uuid = "f6369f11-7733-5829-9624-2563aa707210" -version = "1.3.2" +version = "1.3.3" weakdeps = ["StaticArrays"] [deps.ForwardDiff.extensions] @@ -897,9 +904,9 @@ weakdeps = ["StaticArrays"] [[deps.FreeType2_jll]] deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"] -git-tree-sha1 = "2c5512e11c791d1baed2049c5652441b28fc6a31" +git-tree-sha1 = "70329abc09b886fd2c5d94ad2d9527639c421e3e" uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7" -version = "2.13.4+0" +version = "2.14.3+1" [[deps.FriBidi_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] @@ -913,10 +920,10 @@ uuid = "069b7b12-0de2-55c6-9aab-29f3d0a68a2e" version = "1.1.3" [[deps.FunctionWrappersWrappers]] -deps = ["FunctionWrappers"] -git-tree-sha1 = "b104d487b34566608f8b4e1c39fb0b10aa279ff8" +deps = ["FunctionWrappers", "PrecompileTools", "TruncatedStacktraces"] +git-tree-sha1 = "6874da243fb93e34201d7d4587ffa0e920682f64" uuid = "77dc65aa-8811-40c2-897b-53d922fa7daf" -version = "0.1.3" +version = "1.0.0" [[deps.Future]] deps = ["Random"] @@ -947,15 +954,15 @@ version = "0.2.0" [[deps.GPUCompiler]] deps = ["ExprTools", "InteractiveUtils", "LLVM", "Libdl", "Logging", "PrecompileTools", "Preferences", "Scratch", "Serialization", "TOML", "Tracy", "UUIDs"] -git-tree-sha1 = "966946d226e8b676ca6409454718accb18c34c54" +git-tree-sha1 = "fedfe5e7db7035271c3f58359007f971da1dde87" uuid = "61eb1bfa-7361-4325-ad38-22787b887f55" -version = "1.8.2" +version = "1.9.1" [[deps.GPUToolbox]] deps = ["LLVM"] -git-tree-sha1 = "9e9186b09a13b7f094f87d1a9bb266d8780e1b1c" +git-tree-sha1 = "a589b6c1a0eff953571f5d8b0474f5020831114d" uuid = "096a3bc2-3ced-46d0-87f4-dd12716f4bfc" -version = "1.0.0" +version = "1.1.1" [[deps.GR]] deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Preferences", "Printf", "Qt6Wayland_jll", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "p7zip_jll"] @@ -1059,9 +1066,9 @@ version = "1.13.1+0" [[deps.Hwloc_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "XML2_jll", "Xorg_libpciaccess_jll"] -git-tree-sha1 = "157e2e5838984449e44af851a52fe374d56b9ada" +git-tree-sha1 = "baaaebd42ed9ee1bd9173cfd56910e55a8622ee1" uuid = "e33a78d0-f292-5ffc-b300-72abe9b543c8" -version = "2.13.0+0" +version = "2.13.0+1" [[deps.IOCapture]] deps = ["Logging", "Random"] @@ -1143,9 +1150,9 @@ version = "1.0.0" [[deps.JLD2]] deps = ["ChunkCodecLibZlib", "ChunkCodecLibZstd", "FileIO", "MacroTools", "Mmap", "OrderedCollections", "PrecompileTools", "ScopedValues"] -git-tree-sha1 = "8f8ff711442d1f4cfc0d86133e7ee03d62ec9b98" +git-tree-sha1 = "941f87a0ae1b14d1ac2fa57245425b23a9d7a516" uuid = "033835bb-8acc-5ee8-8aae-3f567f8a3819" -version = "0.6.3" +version = "0.6.4" weakdeps = ["UnPack"] [deps.JLD2.extensions] @@ -1165,9 +1172,9 @@ version = "1.7.1" [[deps.JSON]] deps = ["Dates", "Logging", "Parsers", "PrecompileTools", "StructUtils", "UUIDs", "Unicode"] -git-tree-sha1 = "b3ad4a0255688dcb895a52fafbaae3023b588a90" +git-tree-sha1 = "67c6f1f085cb2671c93fe34244c9cccde30f7a26" uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6" -version = "1.4.0" +version = "1.5.0" [deps.JSON.extensions] JSONArrowExt = ["ArrowTypes"] @@ -1230,9 +1237,9 @@ version = "15.1.0" [[deps.KernelAbstractions]] deps = ["Adapt", "Atomix", "InteractiveUtils", "MacroTools", "PrecompileTools", "Requires", "StaticArrays", "UUIDs"] -git-tree-sha1 = "fb14a863240d62fbf5922bf9f8803d7df6c62dc8" +git-tree-sha1 = "f2e76d3ced51a2a9e185abc0b97494c7273f649f" uuid = "63c18a36-062a-441e-b654-da1e3ab1ce7c" -version = "0.9.40" +version = "0.9.41" weakdeps = ["EnzymeCore", "LinearAlgebra", "SparseArrays"] [deps.KernelAbstractions.extensions] @@ -1254,9 +1261,9 @@ version = "3.100.3+0" [[deps.LDLFactorizations]] deps = ["AMD", "LinearAlgebra", "SparseArrays", "Test"] -git-tree-sha1 = "70f582b446a1c3ad82cf87e62b878668beef9d13" +git-tree-sha1 = "d75c5cb8d6ac9c359ae9eb8e87e446ba9f221dd4" uuid = "40e66cde-538c-5869-a4ad-c39174c6795b" -version = "0.10.1" +version = "0.10.2" [[deps.LERC_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] @@ -1291,12 +1298,6 @@ git-tree-sha1 = "eb62a3deb62fc6d8822c0c4bef73e4412419c5d8" uuid = "1d63c593-3942-5779-bab2-d838dc0a180e" version = "18.1.8+0" -[[deps.LZO_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl"] -git-tree-sha1 = "1c602b1127f4751facb671441ca72715cc95938a" -uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac" -version = "2.10.3+0" - [[deps.LaTeXStrings]] git-tree-sha1 = "dda21b8cbd6a6c40d9d02a73230f9d70fed6918c" uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f" @@ -1344,7 +1345,7 @@ version = "0.6.4" [[deps.LibCURL_jll]] deps = ["Artifacts", "LibSSH2_jll", "Libdl", "OpenSSL_jll", "Zlib_jll", "nghttp2_jll"] uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0" -version = "8.11.1+1" +version = "8.15.0+0" [[deps.LibGit2]] deps = ["LibGit2_jll", "NetworkOptions", "Printf", "SHA"] @@ -1451,10 +1452,10 @@ version = "2.13.0" Metal = "dde4c033-4e86-420c-a63e-0dd931031962" [[deps.LinearSolve]] -deps = ["ArrayInterface", "ChainRulesCore", "ConcreteStructs", "DocStringExtensions", "EnumX", "GPUArraysCore", "InteractiveUtils", "Krylov", "Libdl", "LinearAlgebra", "MKL_jll", "Markdown", "OpenBLAS_jll", "PrecompileTools", "Preferences", "RecursiveArrayTools", "Reexport", "SciMLBase", "SciMLLogging", "SciMLOperators", "Setfield", "StaticArraysCore"] -git-tree-sha1 = "57a7bea58da7de6906f2621294ea35656cb40c5f" +deps = ["ArrayInterface", "ConcreteStructs", "DocStringExtensions", "EnumX", "GPUArraysCore", "InteractiveUtils", "Krylov", "Libdl", "LinearAlgebra", "MKL_jll", "Markdown", "OpenBLAS_jll", "PrecompileTools", "Preferences", "RecursiveArrayTools", "Reexport", "SciMLBase", "SciMLLogging", "SciMLOperators", "Setfield", "StaticArraysCore"] +git-tree-sha1 = "1ddad5f2b0717f71f1588b3519e2f7d80fc2ce65" uuid = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae" -version = "3.66.0" +version = "3.69.0" [deps.LinearSolve.extensions] LinearSolveAMDGPUExt = "AMDGPU" @@ -1465,6 +1466,7 @@ version = "3.66.0" LinearSolveCUDAExt = "CUDA" LinearSolveCUDSSExt = "CUDSS" LinearSolveCUSOLVERRFExt = ["CUSOLVERRF", "SparseArrays"] + LinearSolveChainRulesCoreExt = "ChainRulesCore" LinearSolveCliqueTreesExt = ["CliqueTrees", "SparseArrays"] LinearSolveEnzymeExt = ["EnzymeCore", "SparseArrays"] LinearSolveFastAlmostBandedMatricesExt = "FastAlmostBandedMatrices" @@ -1492,6 +1494,7 @@ version = "3.66.0" CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba" CUDSS = "45b445bb-4962-46a0-9369-b4df9d0f772e" CUSOLVERRF = "a8cc9031-bad2-4722-94f5-40deabb4245c" + ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" CliqueTrees = "60701a23-6482-424a-84db-faee86b9b1f8" EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869" FastAlmostBandedMatrices = "9d29842c-ecb8-4973-b1e9-a27b1157504e" @@ -1569,9 +1572,9 @@ version = "0.5.16" [[deps.MadNCL]] deps = ["Atomix", "KernelAbstractions", "LinearAlgebra", "MadNLP", "NLPModels", "Printf", "Random", "SparseArrays"] -git-tree-sha1 = "fd3e96ec2e760b48084345414b7943a7b607aa0c" +git-tree-sha1 = "8cdb50494fa73f9af44aabadfac51d39413a707e" uuid = "434a0bcb-5a7c-42b2-a9d3-9e3f760e7af0" -version = "0.2.0" +version = "0.2.1" weakdeps = ["MadNLPGPU"] [deps.MadNCL.extensions] @@ -1678,7 +1681,7 @@ version = "0.3.7" [[deps.MozillaCACerts_jll]] uuid = "14a3606d-f60d-562e-9121-12d972cd8159" -version = "2025.5.20" +version = "2025.11.4" [[deps.MuladdMacro]] git-tree-sha1 = "cac9cc5499c25554cba55cd3c30543cff5ca4fab" @@ -1699,9 +1702,9 @@ version = "0.11.2" [[deps.NLPModelsKnitro]] deps = ["KNITRO", "NLPModels", "NLPModelsModifiers", "SolverCore"] -git-tree-sha1 = "f35898a07a02c4f46bc08eca0b19116e894ef464" +git-tree-sha1 = "90e9e12bf859aa3b9453a852015a552592b8ea95" uuid = "bec4dd0d-7755-52d5-9a02-22f0ffc7efcb" -version = "0.10.1" +version = "0.10.2" [[deps.NLPModelsModifiers]] deps = ["FastClosures", "LinearAlgebra", "LinearOperators", "NLPModels", "Printf", "SparseArrays"] @@ -1742,10 +1745,10 @@ uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908" version = "1.3.0" [[deps.NonlinearSolve]] -deps = ["ADTypes", "ArrayInterface", "BracketingNonlinearSolve", "CommonSolve", "ConcreteStructs", "DifferentiationInterface", "FastClosures", "FiniteDiff", "ForwardDiff", "LineSearch", "LinearAlgebra", "LinearSolve", "NonlinearSolveBase", "NonlinearSolveFirstOrder", "NonlinearSolveQuasiNewton", "NonlinearSolveSpectralMethods", "PrecompileTools", "Preferences", "Reexport", "SciMLBase", "SciMLLogging", "SimpleNonlinearSolve", "StaticArraysCore", "SymbolicIndexingInterface"] -git-tree-sha1 = "d27bcf0cebf8786edcc2eaa4455c959e680334e7" +deps = ["ADTypes", "ArrayInterface", "BracketingNonlinearSolve", "CommonSolve", "ConcreteStructs", "DifferentiationInterface", "FastClosures", "FiniteDiff", "ForwardDiff", "LineSearch", "LinearAlgebra", "LinearSolve", "NonlinearSolveBase", "NonlinearSolveFirstOrder", "NonlinearSolveQuasiNewton", "NonlinearSolveSpectralMethods", "PrecompileTools", "Preferences", "Reexport", "SciMLBase", "SciMLLogging", "Setfield", "SimpleNonlinearSolve", "StaticArraysCore", "SymbolicIndexingInterface"] +git-tree-sha1 = "373b688150f160b68083733657246532389e4280" uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec" -version = "4.16.0" +version = "4.17.0" [deps.NonlinearSolve.extensions] NonlinearSolveFastLevenbergMarquardtExt = "FastLevenbergMarquardt" @@ -1775,10 +1778,10 @@ version = "4.16.0" Sundials = "c3572dad-4567-51f8-b174-8c6c989267f4" [[deps.NonlinearSolveBase]] -deps = ["ADTypes", "Adapt", "ArrayInterface", "CommonSolve", "Compat", "ConcreteStructs", "DifferentiationInterface", "EnzymeCore", "FastClosures", "LinearAlgebra", "LogExpFunctions", "Markdown", "MaybeInplace", "PreallocationTools", "Preferences", "Printf", "RecursiveArrayTools", "SciMLBase", "SciMLJacobianOperators", "SciMLLogging", "SciMLOperators", "SciMLStructures", "Setfield", "StaticArraysCore", "SymbolicIndexingInterface", "TimerOutputs"] -git-tree-sha1 = "4f595a0977d6e048fa1e3c382b088b950f8c7934" +deps = ["ADTypes", "Adapt", "ArrayInterface", "CommonSolve", "Compat", "ConcreteStructs", "DifferentiationInterface", "EnzymeCore", "FastClosures", "FunctionWrappers", "FunctionWrappersWrappers", "LinearAlgebra", "LogExpFunctions", "Markdown", "MaybeInplace", "PreallocationTools", "PrecompileTools", "Preferences", "Printf", "RecursiveArrayTools", "SciMLBase", "SciMLJacobianOperators", "SciMLLogging", "SciMLOperators", "SciMLStructures", "Setfield", "StaticArraysCore", "SymbolicIndexingInterface", "TimerOutputs"] +git-tree-sha1 = "7deb924291e30ef27e8823e9d048ffb98ca6ffce" uuid = "be0214bd-f91f-a760-ac4e-3421ce2b2da0" -version = "2.15.0" +version = "2.20.0" [deps.NonlinearSolveBase.extensions] NonlinearSolveBaseBandedMatricesExt = "BandedMatrices" @@ -1869,7 +1872,7 @@ version = "1.6.1" [[deps.OpenSSL_jll]] deps = ["Artifacts", "Libdl"] uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95" -version = "3.5.1+0" +version = "3.5.4+0" [[deps.OpenSpecFun_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl"] @@ -1890,27 +1893,27 @@ version = "1.8.1" [[deps.OrdinaryDiffEq]] deps = ["ADTypes", "Adapt", "ArrayInterface", "CommonSolve", "DataStructures", "DiffEqBase", "DocStringExtensions", "EnumX", "ExponentialUtilities", "FastBroadcast", "FastClosures", "FillArrays", "FiniteDiff", "ForwardDiff", "FunctionWrappersWrappers", "InteractiveUtils", "LineSearches", "LinearAlgebra", "LinearSolve", "Logging", "MacroTools", "MuladdMacro", "NonlinearSolve", "OrdinaryDiffEqAdamsBashforthMoulton", "OrdinaryDiffEqBDF", "OrdinaryDiffEqCore", "OrdinaryDiffEqDefault", "OrdinaryDiffEqDifferentiation", "OrdinaryDiffEqExplicitRK", "OrdinaryDiffEqExponentialRK", "OrdinaryDiffEqExtrapolation", "OrdinaryDiffEqFIRK", "OrdinaryDiffEqFeagin", "OrdinaryDiffEqFunctionMap", "OrdinaryDiffEqHighOrderRK", "OrdinaryDiffEqIMEXMultistep", "OrdinaryDiffEqLinear", "OrdinaryDiffEqLowOrderRK", "OrdinaryDiffEqLowStorageRK", "OrdinaryDiffEqNonlinearSolve", "OrdinaryDiffEqNordsieck", "OrdinaryDiffEqPDIRK", "OrdinaryDiffEqPRK", "OrdinaryDiffEqQPRK", "OrdinaryDiffEqRKN", "OrdinaryDiffEqRosenbrock", "OrdinaryDiffEqSDIRK", "OrdinaryDiffEqSSPRK", "OrdinaryDiffEqStabilizedIRK", "OrdinaryDiffEqStabilizedRK", "OrdinaryDiffEqSymplecticRK", "OrdinaryDiffEqTsit5", "OrdinaryDiffEqVerner", "Polyester", "PreallocationTools", "PrecompileTools", "Preferences", "RecursiveArrayTools", "Reexport", "SciMLBase", "SciMLOperators", "SciMLStructures", "SimpleNonlinearSolve", "SparseArrays", "Static", "StaticArrayInterface", "StaticArrays", "TruncatedStacktraces"] -git-tree-sha1 = "924e1db15095c7df6b844231c00c40d756a7553d" +git-tree-sha1 = "47271adac597af08263b6ea2669e93040b45c4d0" uuid = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed" -version = "6.108.0" +version = "6.111.0" [[deps.OrdinaryDiffEqAdamsBashforthMoulton]] deps = ["DiffEqBase", "FastBroadcast", "MuladdMacro", "OrdinaryDiffEqCore", "OrdinaryDiffEqLowOrderRK", "Polyester", "RecursiveArrayTools", "Reexport", "SciMLBase", "Static"] -git-tree-sha1 = "8307937159c3aeec5f19f4b661d82d96d25a3ff1" +git-tree-sha1 = "2e44acb684dfcdc2e41851a988733e30b28a8478" uuid = "89bda076-bce5-4f1c-845f-551c83cdda9a" -version = "1.9.0" +version = "1.11.0" [[deps.OrdinaryDiffEqBDF]] deps = ["ADTypes", "ArrayInterface", "DiffEqBase", "FastBroadcast", "LinearAlgebra", "MacroTools", "MuladdMacro", "OrdinaryDiffEqCore", "OrdinaryDiffEqDifferentiation", "OrdinaryDiffEqNonlinearSolve", "OrdinaryDiffEqSDIRK", "PrecompileTools", "Preferences", "RecursiveArrayTools", "Reexport", "SciMLBase", "StaticArrays", "TruncatedStacktraces"] -git-tree-sha1 = "22b0c4f7939af140b7f7f4ce2cce90d9f72fa515" +git-tree-sha1 = "8ebd2eb20a8ebb12911b40282d5b41e2db6d107b" uuid = "6ad6398a-0878-4a85-9266-38940aa047c8" -version = "1.22.0" +version = "1.24.0" [[deps.OrdinaryDiffEqCore]] -deps = ["ADTypes", "Accessors", "Adapt", "ArrayInterface", "ConcreteStructs", "DataStructures", "DiffEqBase", "DocStringExtensions", "EnumX", "EnzymeCore", "FastBroadcast", "FastClosures", "FastPower", "FillArrays", "FunctionWrappersWrappers", "InteractiveUtils", "LinearAlgebra", "Logging", "MacroTools", "MuladdMacro", "Polyester", "PrecompileTools", "Preferences", "Random", "RecursiveArrayTools", "Reexport", "SciMLBase", "SciMLLogging", "SciMLOperators", "SciMLStructures", "Static", "StaticArrayInterface", "StaticArraysCore", "SymbolicIndexingInterface", "TruncatedStacktraces"] -git-tree-sha1 = "b4a8d9b96931c2fc69126233bbe6d1a11b053d77" +deps = ["ADTypes", "Accessors", "Adapt", "ArrayInterface", "ConcreteStructs", "DataStructures", "DiffEqBase", "DocStringExtensions", "EnumX", "EnzymeCore", "FastBroadcast", "FastClosures", "FastPower", "FunctionWrappersWrappers", "InteractiveUtils", "LinearAlgebra", "Logging", "MacroTools", "MuladdMacro", "Polyester", "PrecompileTools", "Preferences", "Random", "RecursiveArrayTools", "Reexport", "SciMLBase", "SciMLLogging", "SciMLOperators", "SciMLStructures", "Static", "StaticArraysCore", "SymbolicIndexingInterface", "TruncatedStacktraces"] +git-tree-sha1 = "73e431f66fb9854474c0bec1c11053e8889629c1" uuid = "bbf590c4-e513-4bbe-9b18-05decba2e5d8" -version = "3.22.0" +version = "3.27.0" [deps.OrdinaryDiffEqCore.extensions] OrdinaryDiffEqCoreMooncakeExt = "Mooncake" @@ -1922,15 +1925,15 @@ version = "3.22.0" [[deps.OrdinaryDiffEqDefault]] deps = ["ADTypes", "DiffEqBase", "EnumX", "LinearAlgebra", "LinearSolve", "OrdinaryDiffEqBDF", "OrdinaryDiffEqCore", "OrdinaryDiffEqRosenbrock", "OrdinaryDiffEqTsit5", "OrdinaryDiffEqVerner", "PrecompileTools", "Preferences", "Reexport", "SciMLBase"] -git-tree-sha1 = "0f40d969dd10d1b226c864bf7dc4b4b8933bc130" +git-tree-sha1 = "5fbd116f93790ce79c4beff8206e1b8e45c492a2" uuid = "50262376-6c5a-4cf5-baba-aaf4f84d72d7" -version = "1.13.0" +version = "1.14.0" [[deps.OrdinaryDiffEqDifferentiation]] -deps = ["ADTypes", "ArrayInterface", "ConcreteStructs", "ConstructionBase", "DiffEqBase", "DifferentiationInterface", "FastBroadcast", "FiniteDiff", "ForwardDiff", "FunctionWrappersWrappers", "LinearAlgebra", "LinearSolve", "OrdinaryDiffEqCore", "SciMLBase", "SciMLOperators", "SparseMatrixColorings", "StaticArrayInterface", "StaticArrays"] -git-tree-sha1 = "c85968ea296acaff5de6ed0d9b64ddb00f4ea01f" +deps = ["ADTypes", "ArrayInterface", "ConcreteStructs", "ConstructionBase", "DiffEqBase", "DifferentiationInterface", "FastBroadcast", "FiniteDiff", "ForwardDiff", "FunctionWrappersWrappers", "LinearAlgebra", "LinearSolve", "OrdinaryDiffEqCore", "SciMLBase", "SciMLOperators", "SparseMatrixColorings", "StaticArrays"] +git-tree-sha1 = "c7d06493d3327cc45f0d8d7e641203d28779e837" uuid = "4302a76b-040a-498a-8c04-15b101fed76b" -version = "2.2.1" +version = "2.6.0" weakdeps = ["SparseArrays"] [deps.OrdinaryDiffEqDifferentiation.extensions] @@ -1938,153 +1941,153 @@ weakdeps = ["SparseArrays"] [[deps.OrdinaryDiffEqExplicitRK]] deps = ["DiffEqBase", "FastBroadcast", "LinearAlgebra", "MuladdMacro", "OrdinaryDiffEqCore", "RecursiveArrayTools", "Reexport", "SciMLBase", "TruncatedStacktraces"] -git-tree-sha1 = "c5b900878b088776b8d1bd5a7b1d94e301e21c4e" +git-tree-sha1 = "17d8bfeab9d6a7b31d116e950aa7204fd444ec19" uuid = "9286f039-9fbf-40e8-bf65-aa933bdc4db0" -version = "1.9.0" +version = "1.11.0" [[deps.OrdinaryDiffEqExponentialRK]] deps = ["ADTypes", "DiffEqBase", "ExponentialUtilities", "FastBroadcast", "LinearAlgebra", "MuladdMacro", "OrdinaryDiffEqCore", "OrdinaryDiffEqDifferentiation", "RecursiveArrayTools", "Reexport", "SciMLBase"] -git-tree-sha1 = "72156f954b199ff23dada0e8c0f12c44503b5cf9" +git-tree-sha1 = "32fb54c8000c82fd32c55f7bf52f4651a3bd0e61" uuid = "e0540318-69ee-4070-8777-9e2de6de23de" -version = "1.13.0" +version = "1.15.0" [[deps.OrdinaryDiffEqExtrapolation]] deps = ["ADTypes", "DiffEqBase", "FastBroadcast", "FastPower", "LinearSolve", "MuladdMacro", "OrdinaryDiffEqCore", "OrdinaryDiffEqDifferentiation", "Polyester", "RecursiveArrayTools", "Reexport", "SciMLBase"] -git-tree-sha1 = "129730b7b6cb60cc9c18e0db5861f4a7ed2c30b9" +git-tree-sha1 = "57bf89f5b144f6e5af1146fb7aee1544c6b76950" uuid = "becaefa8-8ca2-5cf9-886d-c06f3d2bd2c4" -version = "1.16.0" +version = "1.18.0" [[deps.OrdinaryDiffEqFIRK]] deps = ["ADTypes", "DiffEqBase", "FastBroadcast", "FastGaussQuadrature", "FastPower", "LinearAlgebra", "LinearSolve", "MuladdMacro", "OrdinaryDiffEqCore", "OrdinaryDiffEqDifferentiation", "OrdinaryDiffEqNonlinearSolve", "Polyester", 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"FastBroadcast", "MuladdMacro", "OrdinaryDiffEqCore", "RecursiveArrayTools", "Reexport", "SciMLBase", "StaticArrays"] -git-tree-sha1 = "d156a972fa7bc37bf8377d33a7d51d152e354d4c" +git-tree-sha1 = "bda2155c5abd7b1e4965d35f930f78e320d7bafe" uuid = "358294b1-0aab-51c3-aafe-ad5ab194a2ad" -version = "1.8.0" +version = "1.10.0" [[deps.OrdinaryDiffEqSymplecticRK]] deps = ["DiffEqBase", "FastBroadcast", "MuladdMacro", "OrdinaryDiffEqCore", "Polyester", "RecursiveArrayTools", "Reexport", "SciMLBase"] -git-tree-sha1 = "9b783806fe2dc778649231cb3932cb71b63222d9" +git-tree-sha1 = "b18a4e7973e73e84cfd79222e2389565b323b588" uuid = "fa646aed-7ef9-47eb-84c4-9443fc8cbfa8" -version = "1.11.0" +version = "1.13.0" [[deps.OrdinaryDiffEqTsit5]] deps = ["DiffEqBase", "FastBroadcast", "LinearAlgebra", "MuladdMacro", "OrdinaryDiffEqCore", "PrecompileTools", "Preferences", "RecursiveArrayTools", "Reexport", "SciMLBase", "Static", "TruncatedStacktraces"] -git-tree-sha1 = "8be4cba85586cd2efa6c76d1792c548758610901" +git-tree-sha1 = "b305a813cc926ce31458e2b955612d9b719f1c38" uuid = "b1df2697-797e-41e3-8120-5422d3b24e4a" -version = "1.9.0" +version = "1.11.0" [[deps.OrdinaryDiffEqVerner]] deps = ["DiffEqBase", "FastBroadcast", "LinearAlgebra", "MuladdMacro", "OrdinaryDiffEqCore", "Polyester", "PrecompileTools", "Preferences", "RecursiveArrayTools", "Reexport", "SciMLBase", "Static", "TruncatedStacktraces"] -git-tree-sha1 = "5ca5dbbfea89e14f283ce9fe2301c528ff4ec007" +git-tree-sha1 = "918dbbaeea6684d4d65907994650d9614bdd2eb2" uuid = "79d7bb75-1356-48c1-b8c0-6832512096c2" -version = "1.11.0" +version = "1.13.0" [[deps.PCRE2_jll]] deps = ["Artifacts", "Libdl"] @@ -2118,7 +2121,7 @@ version = "0.44.2+0" [[deps.Pkg]] deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "Random", "SHA", "TOML", "Tar", "UUIDs", "p7zip_jll"] uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" -version = "1.12.0" +version = "1.12.1" weakdeps = ["REPL"] [deps.Pkg.extensions] @@ -2176,9 +2179,9 @@ version = "1.4.3" [[deps.PreallocationTools]] deps = ["Adapt", "ArrayInterface", "PrecompileTools"] -git-tree-sha1 = "dc8d6bde5005a0eac05ae8faf1eceaaca166cfa4" +git-tree-sha1 = "e16b73bf892c55d16d53c9c0dbd0fb31cb7e25da" uuid = "d236fae5-4411-538c-8e31-a6e3d9e00b46" -version = "1.1.2" +version = "1.2.0" weakdeps = ["ForwardDiff", "ReverseDiff", "SparseConnectivityTracer"] [deps.PreallocationTools.extensions] @@ -2200,9 +2203,9 @@ version = "1.5.2" [[deps.PrettyTables]] deps = ["Crayons", "LaTeXStrings", "Markdown", "PrecompileTools", "Printf", "REPL", "Reexport", "StringManipulation", "Tables"] -git-tree-sha1 = "211530a7dc76ab59087f4d4d1fc3f086fbe87594" +git-tree-sha1 = "624de6279ab7d94fc9f672f0068107eb6619732c" uuid = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d" -version = "3.2.3" +version = "3.3.2" [deps.PrettyTables.extensions] PrettyTablesTypstryExt = "Typstry" @@ -2286,9 +2289,9 @@ version = "0.6.12" [[deps.RecursiveArrayTools]] deps = ["Adapt", "ArrayInterface", "DocStringExtensions", "GPUArraysCore", "LinearAlgebra", "PrecompileTools", "RecipesBase", "StaticArraysCore", "SymbolicIndexingInterface"] -git-tree-sha1 = "18d2a6fd1ea9a8205cadb3a5704f8e51abdd748b" +git-tree-sha1 = "e4fd3369c78666a65ccec25dba28a0b181434ab2" uuid = "731186ca-8d62-57ce-b412-fbd966d074cd" -version = "3.48.0" +version = "3.52.0" [deps.RecursiveArrayTools.extensions] RecursiveArrayToolsFastBroadcastExt = "FastBroadcast" @@ -2370,9 +2373,9 @@ version = "2025.9.18+0" [[deps.SciMLBase]] deps = ["ADTypes", "Accessors", "Adapt", "ArrayInterface", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "EnumX", "FunctionWrappersWrappers", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "Markdown", "Moshi", "PreallocationTools", "PrecompileTools", "Preferences", "Printf", "RecipesBase", "RecursiveArrayTools", "Reexport", "RuntimeGeneratedFunctions", "SciMLLogging", "SciMLOperators", "SciMLPublic", "SciMLStructures", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface"] -git-tree-sha1 = "0be0208add9b6836a701e0ac3ad30bda72fee51d" +git-tree-sha1 = "908c0bf271604d09393a21c142116ab26f66f67c" uuid = "0bca4576-84f4-4d90-8ffe-ffa030f20462" -version = "2.150.0" +version = "2.154.0" [deps.SciMLBase.extensions] SciMLBaseChainRulesCoreExt = "ChainRulesCore" @@ -2553,9 +2556,9 @@ version = "1.2.1" [[deps.SparseMatrixColorings]] deps = ["ADTypes", "DocStringExtensions", "LinearAlgebra", "PrecompileTools", "Random", "SparseArrays"] -git-tree-sha1 = "fa43a02c01e3e3cb065c89bf9b648b89e3c06f18" +git-tree-sha1 = "1c1be8c6fdfaf9b6c9e156c509e672953b8e6af7" uuid = "0a514795-09f3-496d-8182-132a7b665d35" -version = "0.4.25" +version = "0.4.26" [deps.SparseMatrixColorings.extensions] SparseMatrixColoringsCUDAExt = "CUDA" @@ -2572,9 +2575,9 @@ version = "0.4.25" [[deps.SpecialFunctions]] deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"] -git-tree-sha1 = "5acc6a41b3082920f79ca3c759acbcecf18a8d78" +git-tree-sha1 = "2700b235561b0335d5bef7097a111dc513b8655e" uuid = "276daf66-3868-5448-9aa4-cd146d93841b" -version = "2.7.1" +version = "2.7.2" weakdeps = ["ChainRulesCore"] [deps.SpecialFunctions.extensions] @@ -2664,16 +2667,18 @@ version = "1.11.0" [[deps.StructUtils]] deps = ["Dates", "UUIDs"] -git-tree-sha1 = "28145feabf717c5d65c1d5e09747ee7b1ff3ed13" +git-tree-sha1 = "fa95b3b097bcef5845c142ea2e085f1b2591e92c" uuid = "ec057cc2-7a8d-4b58-b3b3-92acb9f63b42" -version = "2.6.3" +version = "2.7.1" [deps.StructUtils.extensions] StructUtilsMeasurementsExt = ["Measurements"] + StructUtilsStaticArraysCoreExt = ["StaticArraysCore"] StructUtilsTablesExt = ["Tables"] [deps.StructUtils.weakdeps] Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7" + StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c" Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c" [[deps.StyledStrings]] @@ -2800,9 +2805,9 @@ version = "0.4.1" [[deps.UnoSolver]] deps = ["LinearAlgebra", "OpenBLAS32_jll", "Uno_jll"] -git-tree-sha1 = "cf39af9c8be02fd5f5027bc3184e8582b8f6d2a0" +git-tree-sha1 = "a947341afb633f09cdcf875090981b80b37ec31f" uuid = "1baa60ac-02f7-4b39-a7a8-2f4f58486b05" -version = "0.2.7" +version = "0.2.10" [deps.UnoSolver.extensions] UnoSolverMathOptInterfaceExt = "MathOptInterface" @@ -2814,14 +2819,14 @@ version = "0.2.7" [[deps.Uno_jll]] deps = ["ASL_jll", "Artifacts", "CompilerSupportLibraries_jll", "HSL_jll", "HiGHS_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl", "METIS_jll", "MUMPS_seq_jll", "SPRAL_jll", "libblastrampoline_jll"] -git-tree-sha1 = "30b1deeaeb5de7c0e0e4a7f9a253195147ed0e9e" +git-tree-sha1 = "3530444c365f78f2d84af6224e4fffbd9e115e49" uuid = "396d5378-14f1-5ab1-981d-48acd51740ed" -version = "2.5.0+0" +version = "2.7.0+0" [[deps.UnsafeAtomics]] -git-tree-sha1 = "b13c4edda90890e5b04ba24e20a310fbe6f249ff" +git-tree-sha1 = "0f30765c32d66d58e41f4cb5624d4fc8a82ec13b" uuid = "013be700-e6cd-48c3-b4a1-df204f14c38f" -version = "0.3.0" +version = "0.3.1" weakdeps = ["LLVM"] [deps.UnsafeAtomics.extensions] @@ -3078,9 +3083,9 @@ version = "1.28.1+0" [[deps.libpng_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"] -git-tree-sha1 = "e015f211ebb898c8180887012b938f3851e719ac" +git-tree-sha1 = "e2a7072fc0cdd7949528c1455a3e5da4122e1153" uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f" -version = "1.6.55+0" +version = "1.6.56+0" [[deps.libva_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll", "Xorg_libXext_jll", "Xorg_libXfixes_jll", "libdrm_jll"] @@ -3112,9 +3117,9 @@ uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e" version = "2022.0.0+1" [[deps.p7zip_jll]] -deps = ["Artifacts", "Libdl"] +deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"] uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" -version = "17.5.0+2" +version = "17.7.0+0" [[deps.x264_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] diff --git a/docs/src/manual-differential-geometry.md b/docs/src/manual-differential-geometry.md index bb102be5..1875f619 100644 --- a/docs/src/manual-differential-geometry.md +++ b/docs/src/manual-differential-geometry.md @@ -1,9 +1,5 @@ # [Differential geometry tools](@id manual-differential-geometry) -```@meta -Draft = false -``` - Optimal control theory relies on differential geometry tools to analyze Hamiltonian systems, compute singular controls, study controllability, and more. This page introduces the main operators available in OptimalControl.jl: Hamiltonian lift, Lie derivatives, Poisson brackets, Lie brackets, and partial time derivatives. !!! note "Type qualification" @@ -221,12 +217,12 @@ f(x, p) = p[1] * x[2] + p[2] * x[1] g(x, p) = x[1]^2 + p[2]^2 # Compute the Poisson bracket -Hfg = Poisson(f, g) +H = Poisson(f, g) # Evaluate at a point x = [1, 2] p = [3, 4] -Hfg(x, p) +H(x, p) ``` ### Verify antisymmetry @@ -247,8 +243,8 @@ println("Sum = ", Hfg(x, p) + Hgf(x, p)) F = OptimalControl.Hamiltonian(f) G = OptimalControl.Hamiltonian(g) -Hfg = Poisson(F, G) -Hfg(x, p) +H = Poisson(F, G) +H(x, p) ``` ### [With keyword arguments](@id poisson-kwargs) @@ -259,8 +255,8 @@ using OptimalControl # hide f(t, x, p) = t + p[1] * x[2] + p[2] * x[1] g(t, x, p) = t^2 + x[1]^2 + p[2]^2 -Hfg = Poisson(f, g; autonomous=false) -Hfg(1, [1, 2], [3, 4]) +H = Poisson(f, g; autonomous=false) +H(1, [1, 2], [3, 4]) ``` ### With Hamiltonian type and keywords @@ -277,8 +273,8 @@ F = OptimalControl.Hamiltonian(f; autonomous=false) G = OptimalControl.Hamiltonian(g; autonomous=false) # No keywords needed here - both Hamiltonians are already non-autonomous -Hfg = Poisson(F, G) -Hfg(1, [1, 2], [3, 4]) +H = Poisson(F, G) +H(1, [1, 2], [3, 4]) ``` ```@example main-9b @@ -291,8 +287,8 @@ F = OptimalControl.Hamiltonian(f; variable=true) G = OptimalControl.Hamiltonian(g; variable=true) # Both are variable, so the Poisson bracket is also variable -Hfg = Poisson(F, G) -Hfg([1, 2], [3, 4], 1) +H = Poisson(F, G) +H([1, 2], [3, 4], 1) ``` ### Relation to Hamiltonian vector fields @@ -320,8 +316,8 @@ HX = Lift(X) HY = Lift(Y) # Poisson bracket of lifts -HXY = Poisson(HX, HY) -HXY([1, 2], [3, 4]) +H = Poisson(HX, HY) +H([1, 2], [3, 4]) ``` This satisfies: $\{H_X, H_Y\} = H_{[X,Y]}$ where $[X,Y]$ is the Lie bracket of vector fields (see next section). @@ -386,14 +382,14 @@ The `@Lie` macro provides a convenient syntax for computing Lie brackets (for ve !!! warning "Important distinction" -- **Square brackets `[...]`** denote **Lie brackets** and work with: - - `VectorField` objects - - Plain Julia functions (automatically wrapped as `VectorField`) -- **Curly braces `{...}`** denote **Poisson brackets** and work with: - - Plain Julia functions (automatically wrapped as `Hamiltonian`) - - `Hamiltonian` objects + - **Square brackets `[...]`** denote **Lie brackets** and work with: + - `VectorField` objects + - Plain Julia functions (automatically wrapped as `VectorField`) + - **Curly braces `{...}`** denote **Poisson brackets** and work with: + - Plain Julia functions (automatically wrapped as `Hamiltonian`) + - `Hamiltonian` objects -When using **only plain functions** (no `VectorField` or `Hamiltonian` objects), specify `autonomous` and/or `variable` keywords as needed to match your function signature. Keywords are optional - if not specified, they use the default values (`autonomous=true`, `variable=false`). If you mix plain functions with `VectorField` or `Hamiltonian` objects, the keywords are inferred from the `VectorField` or `Hamiltonian` objects. + When using **only plain functions** (no `VectorField` or `Hamiltonian` objects), specify `autonomous` and/or `variable` keywords as needed to match your function signature. Keywords are optional - if not specified, they use the default values (`autonomous=true`, `variable=false`). If you mix plain functions with `VectorField` or `Hamiltonian` objects, the keywords are inferred from the `VectorField` or `Hamiltonian` objects. ### Lie brackets with VectorField @@ -467,28 +463,28 @@ Z([1, 2], 1) using OptimalControl # hide X(x) = [0, -x[3], x[2]] Y(x) = [x[3], 0, -x[1]] -Z_func(x) = [x[1], x[2], x[3]] +Z(x) = [x[1], x[2], x[3]] # Nested Lie brackets -nested = @Lie [[X, Y], Z_func] +nested = @Lie [[X, Y], Z] nested([1, 2, 3]) ``` !!! tip "Plain functions vs VectorField" -Using plain functions with `@Lie [X, Y]` is convenient for quick computations. However, if you need to reuse the same vector field multiple times or want explicit control over the autonomy/variability, consider creating `VectorField` objects explicitly: + Using plain functions with `@Lie [X, Y]` is convenient for quick computations. However, if you need to reuse the same vector field multiple times or want explicit control over the autonomy/variability, consider creating `VectorField` objects explicitly: -```julia -# Explicit VectorField (keywords at creation) -X = OptimalControl.VectorField((t, x) -> [t + x[2], -x[1]]; autonomous=false) -Y = OptimalControl.VectorField((t, x) -> [x[1], t*x[2]]; autonomous=false) -Z = @Lie [X, Y] # No keywords needed + ```julia + # Explicit VectorField (keywords at creation) + X = OptimalControl.VectorField((t, x) -> [t + x[2], -x[1]]; autonomous=false) + Y = OptimalControl.VectorField((t, x) -> [x[1], t*x[2]]; autonomous=false) + Z = @Lie [X, Y] # No keywords needed -# Plain functions (keywords at macro call) -X_func(t, x) = [t + x[2], -x[1]] -Y_func(t, x) = [x[1], t*x[2]] -Z = @Lie [X_func, Y_func] autonomous=false -``` + # Plain functions (keywords at macro call) + X(t, x) = [t + x[2], -x[1]] + Y(t, x) = [x[1], t*x[2]] + Z = @Lie [X, Y] autonomous=false + ``` ### Poisson brackets from plain functions From 84deef7160c7a57ec5f1213924007e55d19d1561 Mon Sep 17 00:00:00 2001 From: Olivier Cots Date: Fri, 3 Apr 2026 00:43:06 +0200 Subject: [PATCH 11/11] Improve singular control example documentation - Add comments to control and state bounds in OCP definition - Fix mathematical calculations for singular control derivation - Correct H01, H001, and H101 Poisson bracket calculations - Add non-degeneracy condition proof - Simplify calculation flow and remove redundant steps - Enable draft mode for documentation build --- docs/make.jl | 2 +- docs/src/example-singular-control.md | 92 ++++++++++++++-------------- 2 files changed, 47 insertions(+), 47 deletions(-) diff --git a/docs/make.jl b/docs/make.jl index c9498bcf..29ed025b 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -153,7 +153,7 @@ cp( Draft = false ``` =# -draft = true # Draft mode: if true, @example blocks in markdown are not executed +draft = false # Draft mode: if true, @example blocks in markdown are not executed # ═══════════════════════════════════════════════════════════════════════════════ # Load extensions diff --git a/docs/src/example-singular-control.md b/docs/src/example-singular-control.md index 67c92b28..fb38d094 100644 --- a/docs/src/example-singular-control.md +++ b/docs/src/example-singular-control.md @@ -40,8 +40,8 @@ ocp = @def begin q = (x, y, θ) ∈ R³, state u ∈ R, control - -1 ≤ u(t) ≤ 1 - -π/2 ≤ θ(t) ≤ π/2 + -1 ≤ u(t) ≤ 1 # Control bounds + -π/2 ≤ θ(t) ≤ π/2 # State bounds (helps direct method convergence) x(0) == 0 y(0) == 0 @@ -77,21 +77,21 @@ Let's plot the solution: ```@example main opt = (state_bounds_style=:none, control_bounds_style=:none) -plt = plot(direct_sol; opt..., size=(800, 800)) +plt = plot(direct_sol; label="direct", size=(800, 800), opt...) ``` ## Singular control by hand -The pseudo-Hamiltonian for this time-optimal problem is (with $p^0 = -1$): +The pseudo-Hamiltonian for this time-optimal problem is: ```math -H(q, p, u) = p_1 \cos\theta + p_2(\sin\theta + x) + p_3 u - 1. +H(q, p, u) = p_1 \cos\theta + p_2(\sin\theta + x) + p_3 u. ``` This is control-affine: $H = H_0 + u H_1$ with: ```math -H_0(q, p) = p_1 \cos\theta + p_2(\sin\theta + x) - 1, \quad H_1(q, p) = p_3. +H_0(q, p) = p_1 \cos\theta + p_2(\sin\theta + x), \quad H_1(q, p) = p_3. ``` The switching function is $H_1 = p_3$. On a singular arc, we have $H_1 = 0$ and all its time derivatives must vanish. @@ -110,16 +110,16 @@ H_{01} = \frac{\partial H_0}{\partial p_1} \frac{\partial H_1}{\partial x} - \fr + \frac{\partial H_0}{\partial p_3} \frac{\partial H_1}{\partial \theta} - \frac{\partial H_0}{\partial \theta} \frac{\partial H_1}{\partial p_3}. ``` -Since $H_1 = p_3$ depends only on $p_3$, most terms vanish: +Since $H_1 = p_3$ depends only on $p_3$, the only non-zero contribution comes from the $(\theta, p_3)$ pair: ```math -H_{01} = -\frac{\partial H_0}{\partial \theta} = -(-p_1 \sin\theta + p_2 \cos\theta) = p_1 \sin\theta - p_2 \cos\theta. +H_{01} = \frac{\partial H_0}{\partial \theta} \frac{\partial H_1}{\partial p_3} - \frac{\partial H_0}{\partial p_3} \frac{\partial H_1}{\partial \theta} = (-p_1 \sin\theta + p_2 \cos\theta) \cdot 1 - 0 = -p_1 \sin\theta + p_2 \cos\theta. ``` On the singular arc, $H_{01} = 0$, which gives the constraint: ```math -p_1 \sin\theta = p_2 \cos\theta. +p_2 \cos\theta = p_1 \sin\theta. ``` **Second derivative:** @@ -131,27 +131,23 @@ p_1 \sin\theta = p_2 \cos\theta. For the arc to remain singular, $\dot{H}_{01} = 0$, which gives: ```math -u_s = -\frac{H_{001}}{H_{101}}. +u_s = -\frac{H_{001}}{H_{101}}, ``` -Computing $H_{001}$: +whenever $H_{101} \neq 0$. Computing $H_{001} = \{H_0, H_{01}\}$ with $H_{01} = -p_1 \sin\theta + p_2 \cos\theta$: -```math -H_{001} = \frac{\partial H_0}{\partial p_2} \frac{\partial H_{01}}{\partial \theta} - \frac{\partial H_0}{\partial \theta} \frac{\partial H_{01}}{\partial p_2} - = (\sin\theta + x)(p_1 \cos\theta + p_2 \sin\theta) - (-p_1 \sin\theta + p_2 \cos\theta)(-\cos\theta) - = (\sin\theta + x)(p_1 \cos\theta + p_2 \sin\theta) - p_1 \sin\theta \cos\theta + p_2 \cos^2\theta. -``` - -Since we're on the singular arc where $x$ is part of the state trajectory, we simplify by focusing on the terms involving $p$ and $\theta$. After calculation: +The only non-zero contribution comes from the $(x, p_1)$ pair: ```math -H_{001} = -p_2 \sin\theta. +H_{001} = \frac{\partial H_0}{\partial x} \frac{\partial H_{01}}{\partial p_1} - \frac{\partial H_0}{\partial p_1} \frac{\partial H_{01}}{\partial x} = p_2 \cdot (-\sin\theta) - \cos\theta \cdot 0 = -p_2 \sin\theta. ``` -Computing $H_{101}$: +Computing $H_{101} = \{H_1, H_{01}\}$ with $H_1 = p_3$ and $H_{01} = -p_1 \sin\theta + p_2 \cos\theta$: + +The only non-zero contribution comes from the $(\theta, p_3)$ pair: ```math -H_{101} = \frac{\partial H_1}{\partial p_3} \frac{\partial H_{01}}{\partial \theta} = 1 \cdot (p_1 \cos\theta + p_2 \sin\theta) = p_1 \cos\theta + p_2 \sin\theta. +H_{101} = \frac{\partial H_1}{\partial \theta} \frac{\partial H_{01}}{\partial p_3} - \frac{\partial H_1}{\partial p_3} \frac{\partial H_{01}}{\partial \theta} = 0 - 1 \cdot (-p_1 \cos\theta - p_2 \sin\theta) = p_1 \cos\theta + p_2 \sin\theta. ``` Therefore: @@ -160,24 +156,29 @@ Therefore: u_s = -\frac{H_{001}}{H_{101}} = \frac{p_2 \sin\theta}{p_1 \cos\theta + p_2 \sin\theta}. ``` -**Simplification using the constraint:** +!!! note "Non-degeneracy condition" -From $p_1 \sin\theta = p_2 \cos\theta$, multiply both sides by $\sin\theta$: + We can show that $H_{101} \neq 0$ on the singular arc. From the constraint $p_1 \sin\theta = p_2 \cos\theta$, if we had $H_{101} = p_1 \cos\theta + p_2 \sin\theta = 0$, then: -```math -p_1 \sin^2\theta = p_2 \sin\theta \cos\theta. -``` + ```math + \begin{pmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{pmatrix} + \begin{pmatrix} p_1 \\ p_2 \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \end{pmatrix}. + ``` + + Since this matrix has determinant 1 (hence is invertible), we would have $p_1 = p_2 = 0$. Combined with $p_3 = 0$ (from $H_1 = 0$), this gives $p = 0$, which is impossible for a time-minimization problem. -Substituting into the numerator of $u_s$: +**Simplification using the constraint:** + +Multiply numerator and denominator by $\sin\theta$: ```math -u_s = \frac{p_1 \sin^2\theta}{p_1 \cos\theta \sin\theta + p_1 \sin^2\theta} = \frac{p_1 \sin^2\theta}{p_1(\cos\theta \sin\theta + \sin^2\theta)} = \frac{\sin^2\theta}{\sin\theta(\cos\theta + \sin\theta)} = \sin^2\theta. +u_s = \frac{p_2 \sin^2\theta}{p_1 \cos\theta \sin\theta + p_2 \sin^2\theta}. ``` -Wait, let me recalculate more carefully. From the constraint $p_1 \sin\theta = p_2 \cos\theta$, we have $p_2 = p_1 \tan\theta$. Substituting: +From the constraint $p_1 \sin\theta = p_2 \cos\theta$, we have $p_1 \cos\theta \sin\theta = p_2 \cos^2\theta$. Substituting in the denominator: ```math -u_s = \frac{p_1 \tan\theta \sin\theta}{p_1 \cos\theta + p_1 \tan\theta \sin\theta} = \frac{p_1 \frac{\sin^2\theta}{\cos\theta}}{p_1(\cos\theta + \frac{\sin^2\theta}{\cos\theta})} = \frac{\sin^2\theta}{\cos^2\theta + \sin^2\theta} = \sin^2\theta. +u_s = \frac{p_2 \sin^2\theta}{p_2 \cos^2\theta + p_2 \sin^2\theta} = \frac{p_2 \sin^2\theta}{p_2(\cos^2\theta + \sin^2\theta)} = \sin^2\theta. ``` So the singular control is: @@ -192,7 +193,8 @@ Let's overlay this on the numerical solution: T = time_grid(direct_sol, :control) θ(t) = state(direct_sol)(t)[3] us(t) = sin(θ(t))^2 -plot!(plt, T, us; line=:dash, lw=2, subplot=7, label="us (hand)") +plot!(plt, T, us; subplot=7, line=:dash, lw=2, label="us (hand)") +plot(plt[7]; size=(800, 400)) ``` ## Singular control via Poisson brackets @@ -237,7 +239,8 @@ Let's verify this gives the same result: q(t) = state(direct_sol)(t) p(t) = costate(direct_sol)(t) us_b(t) = us_bracket(q(t), p(t)) -plot!(plt, T, us_b; line=:dashdot, lw=2, subplot=7, label="us (brackets)") +plot!(plt, T, us_b; subplot=7, line=:dashdot, lw=2, label="us (brackets)") +plot(plt[7]; size=(800, 400)) ``` Both methods give the same singular control, which matches the numerical solution from the direct method. @@ -267,13 +270,7 @@ f = Flow(ocp, (x, p, tf) -> u_indirect(x)) nothing # hide ``` -Define the shooting function. We have 5 unknowns: the initial costate $p_0 \in \mathbb{R}^3$, the initial orientation $\theta_0$, and the final time $t_f$. The 5 equations are: - -1. $x(t_f) = 1$ (final position constraint) -2. $y(t_f) = 0$ (final position constraint) -3. $p_\theta(0) = 0$ (transversality condition: $H_1(0) = 0$) -4. $p_\theta(t_f) = 0$ (transversality condition: $H_1(t_f) = 0$) -5. $H(t_f) = 1$ (Hamiltonian constant for time-optimal problems with free final time) +Define the shooting function. We have 5 unknowns: the initial costate $p_0 \in \mathbb{R}^3$, the initial orientation $\theta_0$, and the final time $t_f$. We must define 5 equations to solve for these unknowns. ```@example main t0 = 0 @@ -282,10 +279,10 @@ function shoot!(s, p0, θ0, tf) q_t0, p_t0 = [0, 0, θ0], p0 q_tf, p_tf = f(t0, q_t0, p_t0, tf) - s[1] = q_tf[1] - 1 # x(tf) = 1 - s[2] = q_tf[2] # y(tf) = 0 - s[3] = p_t0[3] # p_θ(0) = 0 - s[4] = p_tf[3] # p_θ(tf) = 0 + s[1] = q_tf[1] - 1 # x(tf) = 1 (boundary condition) + s[2] = q_tf[2] # y(tf) = 0 (boundary condition) + s[3] = p_t0[3] # pθ(0) = 0 (transversality condition) + s[4] = p_tf[3] # pθ(tf) = 0 (transversality condition) # H(tf) = 1 (for time-optimal with p^0 = -1) pxf = p_tf[1] @@ -303,7 +300,10 @@ p0 = costate(direct_sol)(t0) θ0 = state(direct_sol)(t0)[3] tf = variable(direct_sol) -println("Initial guess: p0 = ", p0, ", θ0 = ", θ0, ", tf = ", tf) +println("Initial guess:") +println("p0 = ", p0) +println("θ0 = ", θ0) +println("tf = ", tf) nothing # hide ``` @@ -323,7 +323,7 @@ prob = NonlinearProblem(nle!, ξ_guess) shooting_sol = solve(prob; show_trace=Val(false)) p0_sol, θ0_sol, tf_sol = shooting_sol.u[1:3], shooting_sol.u[4], shooting_sol.u[5] -println("\nShooting solution:") +println("Shooting solution:") println("p0 = ", p0_sol) println("θ0 = ", θ0_sol) println("tf = ", tf_sol) @@ -340,7 +340,7 @@ nothing # hide Plot the indirect solution alongside the direct solution: ```@example main -plot!(plt, indirect_sol; label="Indirect", color=2, linestyle=:dash, opt...) +plot!(plt, indirect_sol; label="indirect", color=2, linestyle=:dash, opt...) ``` The indirect and direct solutions match very well, confirming that our singular control computation is correct.