[Dev] Adding models for exa

[jbcaillau]

Updating foo.jl model into foo2.jl with

• coordinate wise dynamics
• scalar nonlinear (= not ranges) constraints

Allows testing with :exa modeller and Ipopt (mind control-toolbox/CTDirect.jl#475) and MadNLP on CPU, MadNLP on GPU

[ocots]

@jbcaillau To get the OptimalControl model for the beam problem, we have to make:

docp = beam(OptimalControlBackend())

Since, the models for exa are also with OptimalControl, we can have:

docp = beam(OptimalControlBackend(:adnlp))
docp = beam(OptimalControlBackend(:exa))

But now, I have added arguments and keyword arguments to the signature of the problems that are passed to the function CTDirect.direct_transcription, and this function as the following signature:

function direct_transcription(
    ocp::CTModels.Model,
    description...;
    grid_size=__grid_size(),
    disc_method=__disc_method(),
    time_grid=__time_grid(),
    init=__ocp_init(),
    lagrange_to_mayer=true,
    kwargs...,
)

where

[description]: set the NLP model ([`:adnlp`] or `:exa`) and / or solver ([`:ipopt`], :madnlp or :knitro)

so technically, it would be possible to write something like:

docp = beam(OptimalControlBackend(:exa), :adnlp, :madnlp; grid_size=100, disc_method=:euler)

So another possibility is to indicate that the problem is scalarised:

docp = beam(OptimalControlBackend(:scalarised), :adnlp)
docp = beam(OptimalControlBackend(:scalarised), :exa)

and this works too

docp = beam(OptimalControlBackend(), :adnlp) # this is the default

but this does not work:

docp = beam(OptimalControlBackend(), :exa) # the dynamics and constraints must be scalarised.

[jbcaillau]

@ocots just for the record, as of today 🙂: write in dedicated folder foo_s (_s for scalarised) versions of each problem

[jbcaillau]

• share parameters and init between foo and foo_s to avoid inconsistencies

[jbcaillau]

@ocots all models but

• bioreactor (not yet implemented)
• cart_pendulum (not yet implemented)
• dielectrophoretic_particle (not converging)
• moon_lander (not yet implemented)

OK. can you add the associated benchmarks (plots?) to compare with JuMP / OC + ADNLP?