An inverse control problem is formulated as follows: given a set of trajectories and a control system, find a cost such that these paths are optimal. The first question to ask is the uniqueness of the solution of such a problem. For general classes of costs the problem appears to be very difficult, even with a trivial dynamics. We are therefore interested in this issue for the class of costs which are quadratic in the control, when the dynamics depend linearly in the control (Riemannian and sub-Riemannian case). In this case we can reduce the problem to the question of the existence of geodesically equivalent metrics and the existing results will be described, from the theorem of Levi-Civita (1890) to those we obtained recently with Sofya Maslovskaya and Igor Zelenko.

### Séminaire d'Automatique du Plateau de Saclay : Inverse optimal control: the sub-Riemannian case

Séminaire le 24 Mai 2016, 10h00 à CentraleSupelec (Gif-sur-Yvette) Salle du conseil du L2S - B4.40

**Frédéric Jean (ENSTA)**