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Copy file name to clipboardExpand all lines: docs/src/tutorial-basic-example-f.md
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!!! note "Solution and details"
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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.
Copy file name to clipboardExpand all lines: docs/src/tutorial-lqr-basic.md
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nothing # hide
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```
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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.
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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using CTProblems
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## Normalized time
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We consider a [LQR example](@ref) and solve the problem for different values of the final time `tf`.
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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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