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docs/src/dev-ctbase.md

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CollapsedDocStrings = false
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```
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The [CTBase.jl](control-toolbox.org/CTBase.jl/) package is part of the [control-toolbox ecosystem](https://github.com/control-toolbox).
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The [CTBase.jl](https://github.com/control-toolbox/CTBase.jl/) package is part of the [control-toolbox ecosystem](https://github.com/control-toolbox).
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```mermaid
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flowchart TD

docs/src/dev-ctdirect.md

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CollapsedDocStrings = false
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```
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The [CTDirect.jl](control-toolbox.org/CTDirect.jl) package is part of the [control-toolbox ecosystem](https://github.com/control-toolbox).
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The [CTDirect.jl](https://github.com/control-toolbox/CTDirect.jl) package is part of the [control-toolbox ecosystem](https://github.com/control-toolbox).
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```mermaid
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flowchart TD

docs/src/dev-ctflows.md

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CollapsedDocStrings = false
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```
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The [CTFlows.jl](control-toolbox.org/CTFlows.jl) package is part of the [control-toolbox ecosystem](https://github.com/control-toolbox).
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The [CTFlows.jl](https://github.com/control-toolbox/CTFlows.jl) package is part of the [control-toolbox ecosystem](https://github.com/control-toolbox).
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```mermaid
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flowchart TD

docs/src/dev-ctmodels.md

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CollapsedDocStrings = false
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```
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The [CTModels.jl](control-toolbox.org/CTModels.jl) package is part of the [control-toolbox ecosystem](https://github.com/control-toolbox).
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The [CTModels.jl](https://github.com/control-toolbox/CTModels.jl) package is part of the [control-toolbox ecosystem](https://github.com/control-toolbox).
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```mermaid
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flowchart TD

docs/src/dev-ctparser.md

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CollapsedDocStrings = false
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```
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The [CTParser.jl](control-toolbox.org/CTParser.jl) package is part of the [control-toolbox ecosystem](https://github.com/control-toolbox).
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The [CTParser.jl](https://github.com/control-toolbox/CTParser.jl) package is part of the [control-toolbox ecosystem](https://github.com/control-toolbox).
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```mermaid
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flowchart TD

docs/src/dev-optimalcontrol.md

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CollapsedDocStrings = false
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```
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The [OptimalControl.jl](https://control-toolbox.org/OptimalControl.jl) package is part of the [control-toolbox ecosystem](https://github.com/control-toolbox).
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The [OptimalControl.jl](https://github.com/control-toolbox/OptimalControl.jl) package is part of the [control-toolbox ecosystem](https://github.com/control-toolbox).
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```mermaid
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flowchart TD

docs/src/juliacon2024.md

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## Credits (not exhaustive!)
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- [ADNLPModels.jl](https://jso.dev/ADNLPModels.jl)
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- [DifferentiationInterface.jl](https://gdalle.github.io/DifferentiationInterface.jl/DifferentiationInterface/stable)
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- [DifferentialEquations.jl](https://github.com/SciML/DifferentialEquations.jl)
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- [DifferentiationInterface.jl](https://juliadiff.org/DifferentiationInterface.jl/DifferentiationInterface)
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- [DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs)
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- [MLStyle.jl](https://thautwarm.github.io/MLStyle.jl)
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## Acknowledgements

docs/src/tutorial-abstract.md

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- pure Julia (and, as such, effortlessly analysed by the standard Julia parser),
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- as close as possible to the mathematical description of an optimal control problem.
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While the syntax will be transparent to those users familiar with Julia expressions (`Expr`'s), we provide examples for every case that should be widely understandable. We rely heavily on [MLStyle.jl](https://github.com/thautwarm/MLStyle.jl) and its pattern matching abilities 👍🏽 for the semantic pass. Abstract definitions use the macro `@def`.
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While the syntax will be transparent to those users familiar with Julia expressions (`Expr`'s), we provide examples for every case that should be widely understandable. We rely heavily on [MLStyle.jl](https://thautwarm.github.io/MLStyle.jl) and its pattern matching abilities 👍🏽 for the semantic pass. Abstract definitions use the macro `@def`.
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## [Variable](@id tutorial-abstract-variable)
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end
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```
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One (or even the two bounds) can be variable, typically for minimum time problems (see [Mayer cost](#mayer) section):
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One (or even the two bounds) can be variable, typically for minimum time problems (see [Mayer cost](@ref tutorial-abstract-mayer) section):
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```julia
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@def begin

docs/src/tutorial-solve.md

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x0 = [-1, 0]
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ocp = @def begin
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t ∈ [ t0, tf ], time
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x = (q, v) ∈ R², state
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u ∈ R, control
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x(t0) == x0
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x(tf) == [ 0, 0 ]
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ẋ(t) == [ v(t), u(t) ]
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∫( 0.5u(t)^2 ) → min
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end
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nothing # hide
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```
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```@example main
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using NLPModelsIpopt
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solve(ocp)
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```
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\text{minimize}\quad F(y), \quad\text{subject to the constraints}\quad g(y)=0, \quad h(y)\le 0.
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Note: calling `solve` without loading a NLP solver package first will notify the user:
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Calling `solve` without loading a NLP solver package first will notify the user:
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```julia
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julia> solve(ocp)
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ERROR: ExtensionError. Please make: julia> using NLPModelsIpopt
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```
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See below for the NLP solver options.
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## Resolution methods and algorithms
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OptimalControl.jl offers a list of methods to solve your optimal control problem. To get the list of methods, simply call `available_methods`.
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OptimalControl offers a list of methods to solve your optimal control problem. To get the list of methods, simply call `available_methods`.
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```@example main
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available_methods()
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```@example main
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solve(ocp, :madnlp)
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## Direct method
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The options for the direct method are listed in the [`direct_solve`](@ref) keywords.
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The main options, with their [default values], are:
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- `display` ([true], false): setting `display` to false will disable output
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- `grid_size` ([250]): size of the (uniform) time discretization grid. More precisely, it is the number of time steps, that is if `N = grid_size` and if the initial and final times are denoted respectively `t0` and `tf`, then we have `Δt = (tf - t0) / N`
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The options for the direct method are listed [here](https://control-toolbox.org/OptimalControl.jl/stable/dev-ctdirect.html#CTDirect.solve-Tuple{Model,%20Vararg{Symbol}}). The main options, with their [default values], are:
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- `display` ([true], false): setting `display` to false will disable output.
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- `grid_size` ([250]): size of the (uniform) time discretization grid. More precisely, it is the number of time steps, that is if `N = grid_size` and if the initial and final times are denoted respectively `t0` and `tf`, then we have `Δt = (tf - t0) / N`.
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- `disc_method` ([`:trapeze`], `:midpoint`, `:euler`, `:euler_implicit`, `:gauss_legendre_2`, `:gauss_legendre_3`): see [discretisation methods](https://control-toolbox.org/Tutorials.jl/stable/tutorial-discretisation/).
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- `init`: info for the starting guess, which can be provided as numerical values, functions, or an existing solution. See [initial guess tutorial](@ref tutorial-initial-guess).
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For examples of more advanced use, see
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- [discrete continuation]([@ref tutorial-continuation](https://control-toolbox.org/Tutorials.jl/stable/tutorial-continuation/))
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- [discrete continuation](https://control-toolbox.org/Tutorials.jl/stable/tutorial-continuation/)
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- [NLP direct handling](https://control-toolbox.org/Tutorials.jl/stable/tutorial-nlp/)
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docs/src/zhejiang-2025.md

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## Credits (not exhaustive!)
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- [ADNLPModels.jl](https://jso.dev/ADNLPModels.jl)
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- [DifferentiationInterface.jl](https://gdalle.github.io/DifferentiationInterface.jl/DifferentiationInterface/stable)
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- [DifferentialEquations.jl](https://github.com/SciML/DifferentialEquations.jl)
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- [DifferentiationInterface.jl](https://juliadiff.org/DifferentiationInterface.jl/DifferentiationInterface)
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- [DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs)
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- [Ipopt.jl](https://github.com/jump-dev/Ipopt.jl)
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- [MadNLP.jl](https://github.com/MadNLP/MadNLP.jl)
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- [MadNLP.jl](https://madnlp.github.io/MadNLP.jl)
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- [MLStyle.jl](https://thautwarm.github.io/MLStyle.jl)
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## Stand up for science 2025

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