BVP IP

[ocots]

Get code from https://ifpen-gitlab.appcollaboratif.fr/detocs/ipm_ocp

[jbcaillau]

thanks @PlMlsn 🙂

[jbcaillau]

@PlMlsn @ocots made some tests with Olivier code, changing the number of time steps:

• the oscillatory behaviour of the adjoints might be due to the state constraint
• it is fairly different from the other Goddard problem where the adjoints do not oscillate
• changing the tolerance doesn't help
• sims below for 50, 500, 1000 and 4000 points (the last one runs in less than 20s)

Very promising, all in all.

[jbcaillau]

@PlMlsn please point us towards your last paper describing the penalisation technique for state constraints.

The other interesting point is keeping the Hamiltonian maximisation implicit. We also tried it on this problem:
https://ct.gitlabpages.inria.fr/gallery/solarsail/solarsail-simple-version-implicit.html
http://caillau.perso.math.cnrs.fr/research/ocam-2024.pdf (to appear in OCAM)

[PlMlsn]

@jbcaillau the last paper is https://doi.org/10.1051/cocv/2024049 and an arxiv version can be found here https://arxiv.org/pdf/2309.01425

[ocots]

20s for 4000 points. This is nice. It was not like that when I tried few days ago.

[jbcaillau]

Run time for N = 4000 from an N = 2000 sol.

[ocots]

Even with 4000 points we can see that the control is not well approximated at the switching between boundary and singular arcs. Maybe we would need a different scheme.

[jbcaillau]

@PlMlsn @ocots oscillatory behaviour most probably due to an error when parsing the multipliers, check control-toolbox/CTDirect.jl#184

[jbcaillau]

@PlMlsn @ocots oscillatory behaviour most probably due to an error when parsing the multipliers, check control-toolbox/CTDirect.jl#184

@PlMlsn @ocots bug confirmed and corrected (adjoints where not retrieved and plotted properly after the optimisation), see control-toolbox/CTDirect.jl#184

Now, same results as before but without oscillations on the adjoint (N = 50 and N = 1000 below). @ocots your detection (using $H_1$) of the singular arc to initialise shooting should go very smoothly. BTW, worth adding this example as a Goddard no. 2 use case in the tutorials.

[jbcaillau]

hi paul, which one of @PoloMali @PlMlsn is your github id 😅?

if you have some spare (summer) time, our student @ibtissammim who is testing your software on this problem from quantum control (BSBS structure - B = bang, S = singular) might need (and would sure benefit from) some help 🤞🏾! Check control-toolbox/spin#1 (comment)

[PlMlsn]

Hi @jbcaillau, both are mine but the one to use is @PlMlsn. I would be happy to help @ibtissammim on that problem and I hope bvp-dae will be satisfactory :)