Update tutorial files

Author: ocots

docs/src/index.md

@@ -61,4 +61,4 @@ Pkg.status(; mode = PKGMODE_MANIFEST) # hide
 
 ```@raw html
 </details>
-```
+```

docs/src/tutorial-free-times-final-initial.md

@@ -1,9 +1,5 @@
 # [Free initial and final times](@id tutorial-free-times-final-initial)
 
-```@meta
-Draft = false
-```
-
 This tutorial is part of a series on optimal control problems with free time variables.
 See also: [Free final time](@ref tutorial-free-times-final) and [Free initial time](@ref tutorial-free-times-initial).
 

docs/src/tutorial-free-times-final.md

@@ -1,9 +1,5 @@
 # [Optimal control problem with free final time](@id tutorial-free-times-final)
 
-```@meta
-Draft = false
-```
-
 This tutorial is part of a series on optimal control problems with free time variables.
 See also: [Free initial time](@ref tutorial-free-times-initial) and [Free initial and final times](@ref tutorial-free-times-final-initial).
 

docs/src/tutorial-free-times-initial.md

@@ -1,9 +1,5 @@
 # [Optimal control problem with free initial time](@id tutorial-free-times-initial)
 
-```@meta
-Draft = false
-```
-
 This tutorial is part of a series on optimal control problems with free time variables.
 See also: [Free final time](@ref tutorial-free-times-final) and [Free initial and final times](@ref tutorial-free-times-final-initial).
 

docs/src/tutorial-nlp.md

@@ -1,103 +1 @@
-# [NLP and DOCP manipulations](@id tutorial-nlp)
-
-```@meta
-CurrentModule =  OptimalControl
-```
-
-We describe here some more advanced operations related to the discretized optimal control problem.
-When calling `solve(ocp)` three steps are performed internally:
-
-- first, the OCP is discretized into a DOCP (a nonlinear optimization problem),
-- then, this DOCP is solved with a nonlinear programming (NLP) solver, which returns a solution of the discretized problem,
-- finally, a functional solution of the OCP is rebuilt from the solution of the discretized problem.
-
-These steps can also be done separately, for instance if you want to use your own NLP solver. 
-
-Let us load the packages.
-
-```@example main-nlp
-using OptimalControl
-using Plots
-```
-
-We define a test problem
-
-```@example main-nlp
-ocp = @def begin
-
-    t ∈ [0, 1], time
-    x ∈ R², state
-    u ∈ R, control
-
-    x(0) == [ -1, 0 ]
-    x(1) == [ 0, 0 ]
-
-    ẋ(t) == [ x₂(t), u(t) ]
-
-    ∫( 0.5u(t)^2 ) → min
-
-end
-nothing # hide
-```
-
-## Discretization and NLP problem
-
-We discretize the problem with [`direct_transcription`](@extref CTDirect.direct_transcription):
-
-```@example main-nlp
-docp = direct_transcription(ocp)
-nothing # hide
-```
-
-and get the NLP model with [`nlp_model`](@extref CTDirect.nlp_model):
-
-```@example main-nlp
-nlp = nlp_model(docp)
-nothing # hide
-```
-
-The DOCP contains information related to the transcription, including a copy of the original OCP, and the NLP is the resulting discretized nonlinear programming problem, in our case an `ADNLPModel`.
-
-We can now use the solver of our choice to solve it.
-
-## Resolution of the NLP problem
-
-For a first example we use the `ipopt` solver from [NLPModelsIpopt.jl](https://jso.dev/NLPModelsIpopt.jl) package to solve the NLP problem.
-
-```@example main-nlp
-using NLPModelsIpopt
-nlp_sol = ipopt(nlp; print_level=5, mu_strategy="adaptive", tol=1e-8, sb="yes")
-nothing # hide
-```
-
-Then, we can build an optimal control problem solution with [`build_OCP_solution`](@extref CTDirect.build_OCP_solution-Tuple{Any}) (note that the multipliers are optional, but the OCP costate will not be retrieved if the multipliers are not provided) and plot it.
-
-```@example main-nlp
-sol = build_OCP_solution(docp, nlp_sol)
-plot(sol)
-```
-
-## Change the NLP solver
-
-Alternatively, we can use [MadNLP.jl](https://madnlp.github.io/MadNLP.jl) to solve anew the NLP problem:
-
-```@example main-nlp
-using MadNLP
-nlp_sol = madnlp(nlp; print_level=MadNLP.ERROR)
-```
-
-## Initial guess
-
-An initial guess, including warm start, can be passed to [`direct_transcription`](@extref CTDirect.direct_transcription) the same way as for `solve`.
-
-```@example main-nlp
-docp = direct_transcription(ocp; init=sol)
-nothing # hide
-```
-
-It can also be changed after the transcription is done, with  [`set_initial_guess`](@extref CTDirect.set_initial_guess).
-
-```@example main-nlp
-set_initial_guess(docp, sol)
-nothing # hide
-```
+#