[Dev] Add CTDirect.jl test problems

[ocots]

The list of problems is here: https://github.com/control-toolbox/CTDirect.jl/tree/main/test/problems.

[0Yassine0]

@ocots Should we add the full list of problems from CTDirect.jl to the package? And problems are written as OptimalControl models, I suppose we also need to convert it into JuMP models?

[ocots]

@PierreMartinon What do you think?

[0Yassine0]

Here is the list of models from CTDirect :

• [x] beam (simple model)
• [x] bioreactor (from bocop)
• [ ] bolza (simple model)
• [ ] double_integrator (4 different simple models)
• [ ] fuller (simple model)
• [x] goddard
• [x] insurance (from bocop)
• [x] jackson (from bocop)
• [ ] parametric ( a model with a parameter)
• [x] robbins (from bocop)
• [ ] simple_integrator (simple model)
• [ ] swimmer (from bocop)
• [x] vanderpol

[ocots]

C'est très bien on n'ajoute pas les problèmes trop simpliste. Ils seront garder en interne.

[PierreMartinon]

A bit late to the party, sorry.

@ocots, on our last meeting we discussed the issue of the format, eg in CTDirect the problem functions now return a 4-tuple such as

    def goddard begin
     ...
    end

    return ((
        ocp = goddard,
        obj = 1.01257,
        name = "goddard",
        init = (state = [1.01, 0.05, 0.8],),
    ))

Is is unlikely we will find a common format for every framework, but I don't recall what we agreed upon: try to mutualize, have multiple versions of some problems here, or keep separate versions in each package ?