Quasi-optimal robust stabilization of control systems

Christophe Prieur (1) , Emmanuel Trélat (2)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

In this paper, we investigate the problem of semi-global minimal time robust stabilization of analytic control systems with controls entering linearly, by means of a hybrid state feedback law. It is shown that, in the absence of minimal time singular trajectories, the solutions of the closed-loop system converge to the origin in quasi minimal time (for a given bound on the controller) with a robustness property with respect to small measurement noise, external disturbances and actuator noise.

Mots clés: Hybrid feedback; robust stabilization; measurement errors; actuator noise; external disturbances; optimal control; singular trajectory; sub-Riemannian geometry.; sub-Riemannian geometry

Domaines: Optimisation et contrôle [math.OC]

Christophe Prieur, Emmanuel Trélat. Quasi-optimal robust stabilization of control systems. SIAM Journal on Control and Optimization, 2006, 45, pp.1875-1897. ⟨hal-00086384⟩