Semiconcave control-Lyapunov functions and stabiliizing feedbacks

Ludovic Rifford (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

We study the general problem of stabilization of globally asymptotically controllable systems. We construct discontinuous feedback laws, and particularly we make it possible to choose these continuous outside a small set (closed with measure zero) of discontinuity in the case of control systems which are affine in the control; moreover this set of singularities is shown to be repulsive for the Carathéodory solutions of the closed-loop system under an additional assumption.

Domaines: Optimisation et contrôle [math.OC]

Ludovic Rifford. Semiconcave control-Lyapunov functions and stabiliizing feedbacks. SIAM Journal on Control and Optimization, 2002, 41 (3), pp.659-681. ⟨hal-00769001⟩