On the links between relaxation gaps in state-constrained optimal control and a "length explosion" phenomenon in sub-Riemannian geometry

par Nicolas Augier (CNRS, LAAS)

mardi 27 janv. 2026, 11:00 → 13:00 Europe/Paris

Salle Fizeau (LJAD)

In this talk, we address the problem of relaxation gaps in state-constrained optimal control, a well-known difficulty in optimal control theory, particularly in the implementation of numerical methods.

We focus on the role of a "length explosion" phenomenon in sub-Riemannian geometry near the locus where the velocity distribution becomes tangent to the boundary of the constraint, showing that this phenomenon can be responsible for the appearance of relaxation gaps. We conclude by presenting several related open questions.

This presentation is based on joint works with Rodolfo Rios-Zertuche and Milan Korda.