Singular trajectories of driftless and control-affine systems

Yacine Chitour (1) , Frédéric Jean (2) , Emmanuel Trélat (3)

1 L2S - Laboratoire des signaux et systèmes
2 OC - Optimisation et commande
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We establish generic properties for singular trajectories, first for driftless, and then for control-affine systems. We show that, generically -- for the Whitney topology -- nontrivial singular trajectories are of minimal order and of corank one. As a consequence, if the number of vector fields of the system is greater than or equal to 3, then there exists generically no singular minimizing trajectory.

Domaines: Optimisation et contrôle [math.OC]

Yacine Chitour, Frédéric Jean, Emmanuel Trélat. Singular trajectories of driftless and control-affine systems. 44th IEEE Conference on Decision and Control, Dec 2005, seville, Spain. 6 p., ⟨10.1109/cdc.2005.1582278⟩. ⟨hal-00086464⟩