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README.md

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[co-url]: https://codecov.io/gh/control-toolbox/OptimalControl.jl
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[doc-dev-img]: https://img.shields.io/badge/docs-dev-blue.svg
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[doc-dev-url]: https://control-toolbox.org/docs/optimalcontrol/dev/
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[doc-dev-url]: https://control-toolbox.org/OptimalControl.jl/dev/
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[doc-stable-img]: https://img.shields.io/badge/docs-stable-blue.svg
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[doc-stable-url]: https://control-toolbox.org/docs/optimalcontrol/stable/
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[doc-stable-url]: https://control-toolbox.org/OptimalControl.jl/stable/
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[down-img]: https://shields.io/endpoint?url=https://pkgs.genieframework.com/api/v1/badge/OptimalControl
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[down-url]: https://pkgs.genieframework.com?packages=OptimalControl

docs/make.jl

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makedocs(
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warnonly = :cross_references,
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sitename = "OptimalControl.jl",
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format = Documenter.HTML(prettyurls = false,
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size_threshold_ignore = ["api-ctbase.md", "application-mri-saturation.md"]),
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format = Documenter.HTML(
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prettyurls = false,
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size_threshold_ignore = ["api-ctbase.md", "application-mri-saturation.md"],
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assets=[
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asset("https://control-toolbox.org/assets/css/documentation.css"),
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asset("https://control-toolbox.org/assets/js/documentation.js"),
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],
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),
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pages = [
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"Introduction" => "index.md",
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"Tutorials" => [
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],
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"Applications" => [
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"application-batch.md",
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"application-orbit.md",
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"application-sail.md",
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"Catenoid solution" => "application-surface-revolution.md",
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"MRI: saturation problem" => "application-mri-saturation.md",
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],
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"FGS 2024" => "fgs-2024.md",
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"JuliaCon 2024"=> "juliacon2024.md",

docs/src/api-ctbase.md

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# CTBase API
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This is just a dump of CTBase API documentation.
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For more details about `CTBase.jl` package, see the [documentation](https://control-toolbox.org/docs/ctbase).
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For more details about `CTBase.jl` package, see the [documentation](https://control-toolbox.org/CTBase.jl).
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## Index
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docs/src/api-ctdirect.md

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# CTDirect API
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This is just a dump of CTDirect API documentation.
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For more details about `CTDirect.jl` package, see the [documentation](https://control-toolbox.org/docs/ctdirect).
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For more details about `CTDirect.jl` package, see the [documentation](https://control-toolbox.org/CTDirect.jl).
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## Index
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docs/src/api-ctflows.md

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# CTFlows API
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This is just a dump of CTFlows API documentation.
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For more details about `CTFlows.jl` package, see the [documentation](https://control-toolbox.org/docs/ctflows).
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For more details about `CTFlows.jl` package, see the [documentation](https://control-toolbox.org/CTFlows.jl).
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## Index
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docs/src/api-ctproblems.md

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# CTProblems API
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This is just a dump of CTProblems API documentation.
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For more details about `CTProblems.jl` package, see the [documentation](https://control-toolbox.org/docs/ctproblems).
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For more details about `CTProblems.jl` package, see the [documentation](https://control-toolbox.org/CTProblems.jl).
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## Index
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docs/src/application-mri-saturation.md

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docs/src/fgs-2024.md

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- New applications (biology, space mechanics, quantum mechanics and more)
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- Additional solvers: direct shooting, collocation for BVP, Hamiltonian pathfollowing...
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- ... and open to contributions!
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- [CTProblems.jl](https://control-toolbox.org/docs/ctproblems/stable/problems-list.html)
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- [CTProblems.jl](https://control-toolbox.org/CTProblems.jl/stable/problems-list.html)
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# control-toolbox.org
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- Open toolbox
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- Collection of Julia Packages rooted at [OptimalControl.jl](https://control-toolbox.org/docs/optimalcontrol)
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- Collection of Julia Packages rooted at [OptimalControl.jl](https://control-toolbox.org/OptimalControl.jl)
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```@raw html
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<a href="https://control-toolbox.org"><img width="800" alt="control-toolbox.org" src="./assets/control-toolbox.jpg"></a>

docs/src/index.md

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```mermaid
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flowchart TD
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O(<a href='https://control-toolbox.org/docs/optimalcontrol/stable/'>OptimalControl</a>) --> B(<a href='https://control-toolbox.org/docs/ctbase/stable/'>CTBase</a>)
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O --> D(<a href='https://control-toolbox.org/docs/ctdirect/stable/'>CTDirect</a>)
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O --> F(<a href='https://control-toolbox.org/docs/ctflows/stable/'>CTFlows</a>)
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P(<a href='https://control-toolbox.org/docs/ctproblems/stable/'>CTProblems</a>) --> F
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O(<a href='https://control-toolbox.org/OptimalControl.jl/stable/'>OptimalControl</a>) --> B(<a href='https://control-toolbox.org/CTBase.jl/stable/'>CTBase</a>)
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O --> D(<a href='https://control-toolbox.org/CTDirect.jl/stable/'>CTDirect</a>)
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O --> F(<a href='https://control-toolbox.org/CTFlows.jl/stable/'>CTFlows</a>)
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P(<a href='https://control-toolbox.org/CTProblems.jl/stable/'>CTProblems</a>) --> F
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P --> B
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F --> B
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D --> B

docs/src/juliacon2023.md

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- [Coupling direct and indirect solvers, examples](https://ct.gitlabpages.inria.fr/gallery//notebooks.html)
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# OptimalControl.jl
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- [Basic example: double integrator](https://control-toolbox.org/docs/optimalcontrol/dev/tutorial-basic-example-f.html)
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- [Basic example: double integrator (cont'ed)](https://control-toolbox.org/docs/optimalcontrol/dev/tutorial-basic-example.html)
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- [Advanced example: Goddard problem](https://control-toolbox.org/docs/optimalcontrol/dev/tutorial-goddard.html)
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- [Basic example: double integrator](https://control-toolbox.org/OptimalControl.jl/dev/tutorial-basic-example-f.html)
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- [Basic example: double integrator (cont'ed)](https://control-toolbox.org/OptimalControl.jl/dev/tutorial-basic-example.html)
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- [Advanced example: Goddard problem](https://control-toolbox.org/OptimalControl.jl/dev/tutorial-goddard.html)
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# Wrap up
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- [X] High level modelling of optimal control problems
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- [ct_repl](./assets/repl.mp4)
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- Additional solvers: direct shooting, collocation for BVP, Hamiltonian pathfollowing...
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- ... and open to contributions!
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- [CTProblems.jl](https://control-toolbox.org/docs/ctproblems/stable/problems-list.html)
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- [CTProblems.jl](https://control-toolbox.org/CTProblems.jl/stable/problems-list.html)
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# control-toolbox.org
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- Open toolbox
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- Collection of Julia Packages rooted at [OptimalControl.jl](https://control-toolbox.org/docs/optimalcontrol)
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- Collection of Julia Packages rooted at [OptimalControl.jl](https://control-toolbox.org/OptimalControl.jl)
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```@raw html
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<a href="https://control-toolbox.org"><img width="800" alt="control-toolbox.org" src="./assets/control-toolbox.jpg"></a>

docs/src/juliacon2024.md

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## control-toolbox.org
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- Open toolbox
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- Collection of Julia Packages rooted at [OptimalControl.jl](https://control-toolbox.org/docs/optimalcontrol)
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- Collection of Julia Packages rooted at [OptimalControl.jl](https://control-toolbox.org/OptimalControl.jl)
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```@raw html
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<a href="https://control-toolbox.org"><img width="800" alt="control-toolbox.org" src="./assets/control-toolbox.jpg"></a>

docs/src/juliaopt2023.md

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# OptimalControl.jl
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- [Basic example: double integrator (1/3)](https://control-toolbox.org/docs/optimalcontrol/dev/tutorial-basic-example-f.html)
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- [Basic example: double integrator (2/3)](https://control-toolbox.org/docs/optimalcontrol/dev/tutorial-basic-example.html)
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- [Basic example: double integrator (3/3)](https://control-toolbox.org/docs/optimalcontrol/dev/tutorial-double-integrator.html)
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- [Indirect simple shooting](https://control-toolbox.org/docs/optimalcontrol/dev/tutorial-iss.html)
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- [Advanced example: Goddard problem](https://control-toolbox.org/docs/optimalcontrol/dev/tutorial-goddard.html)
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- [Basic example: double integrator (1/3)](https://control-toolbox.org/OptimalControl.jl/dev/tutorial-basic-example-f.html)
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- [Basic example: double integrator (2/3)](https://control-toolbox.org/OptimalControl.jl/dev/tutorial-basic-example.html)
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- [Basic example: double integrator (3/3)](https://control-toolbox.org/OptimalControl.jl/dev/tutorial-double-integrator.html)
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- [Indirect simple shooting](https://control-toolbox.org/OptimalControl.jl/dev/tutorial-iss.html)
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- [Advanced example: Goddard problem](https://control-toolbox.org/OptimalControl.jl/dev/tutorial-goddard.html)
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# Wrap up
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- [ct_repl](./assets/repl.mp4)
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- Additional solvers: direct shooting, collocation for BVP, Hamiltonian pathfollowing...
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- ... and open to contributions!
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- [CTProblems.jl](https://control-toolbox.org/docs/ctproblems/stable/problems-list.html)
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- [CTProblems.jl](https://control-toolbox.org/CTProblems.jl/stable/problems-list.html)
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# control-toolbox.org
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- Open toolbox
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- Collection of Julia Packages rooted at [OptimalControl.jl](https://control-toolbox.org/docs/optimalcontrol)
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- Collection of Julia Packages rooted at [OptimalControl.jl](https://control-toolbox.org/OptimalControl.jl)
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```@raw html
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<a href="https://control-toolbox.org"><img width="800" alt="control-toolbox.org" src="./assets/control-toolbox.jpg"></a>

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docs/src/tutorial-basic-example-f.md

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See the page
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[Double integrator: energy minimisation](https://control-toolbox.org/docs/ctproblems/stable/problems/double_integrator_energy.html#DIE)
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[Double integrator: energy minimisation](https://control-toolbox.org/CTProblems.jl/stable/problems/double_integrator_energy.html#DIE)
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for the analytical solution and details about this problem.
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First, we need to import the `OptimalControl.jl` package to define the optimal control problem and `NLPModelsIpopt.jl` to solve it.
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!!! note "Nota bene"
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There are two ways to define an optimal control problem:
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- using functions like in this example, see also the [`Model` documentation](https://control-toolbox.org/docs/ctbase/stable/api-model.html) for more details.
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- using functions like in this example, see also the [`Model` documentation](https://control-toolbox.org/CTBase.jl/stable/api-model.html) for more details.
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- using an abstract formulation, see for instance [basic example](@ref basic) to compare.
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Solve it

docs/src/tutorial-basic-example.md

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See the page
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[Double integrator: energy minimisation](https://control-toolbox.org/docs/ctproblems/stable/problems/double_integrator_energy.html#DIE)
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[Double integrator: energy minimisation](https://control-toolbox.org/CTProblems.jl/stable/problems/double_integrator_energy.html#DIE)
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for the analytical solution and details about this problem.
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First, we need to import the `OptimalControl.jl` package to define the optimal control problem and `NLPModelsIpopt.jl` to solve it.

docs/src/tutorial-goddard.md

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which is the reason why we use the `@Lie` macro to compute Poisson brackets below.
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With the help of the [differential geometry primitives](https://control-toolbox.org/CTBase.jl/stable/api-diffgeom.html)
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from [CTBase.jl](https://control-toolbox.org/CTBase.jl),
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```@example main

docs/src/tutorial-lqr-basic.md

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We plot the state and control variables considering a normalized time $s=(t-t_0)/(t_f-t_0)$, thanks to the keyword argument `time=:normalized` of the [plot](https://control-toolbox.org/docs/ctbase/stable/api-plot.html) function.
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We plot the state and control variables considering a normalized time $s=(t-t_0)/(t_f-t_0)$, thanks to the keyword argument `time=:normalized` of the [plot](https://control-toolbox.org/CTBase.jl/stable/api-plot.html) function.
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```@example main
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docs/src/tutorial-plot.md

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## Plot the norm of the control
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For some problem, it is interesting to plot the norm of the control. You can do it by using the `control` optional keyword argument with `:norm` value. The default value is `:components`. Let us illustrate this on the consumption minimisation orbital transfer problem from [CTProlbems.jl](https://control-toolbox.org/docs/ctproblems).
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For some problem, it is interesting to plot the norm of the control. You can do it by using the `control` optional keyword argument with `:norm` value. The default value is `:components`. Let us illustrate this on the consumption minimisation orbital transfer problem from [CTProlbems.jl](https://control-toolbox.org/CTProblems.jl).
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```@example main
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Then, we plot the solutions on the same figure considering a normalized time $s=(t-t_0)/(t_f-t_0)$, thanks to the keyword argument `time=:normalized` of the [plot](https://control-toolbox.org/docs/ctbase/stable/api-plot.html) function.
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Then, we plot the solutions on the same figure considering a normalized time $s=(t-t_0)/(t_f-t_0)$, thanks to the keyword argument `time=:normalized` of the [plot](https://control-toolbox.org/CTBase.jl/stable/api-plot.html) function.
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```@example main
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