Controle optimal Optimal Control

Controle optimal / Optimal Control Stabilisation des systemes globalement asymptotiquement com- mandables Ludovic Rifford Institut Girard Desargues, Universite Claude Bernard Lyon I 43, boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex. Courriel: Resume. Etant donne un systeme commande globalement asymptotiquement commandable a l'origine, nous deduisons d'un theoreme d'existence de fonction Lyapunov semiconcave, la construction d'un retour d'etat globa- lement asymptotiquement stabilisant au sens des solutions Euler. Celui- ci se trouve etre assez regulier dans le cas des systemes affines en la commande. Stabilization of globally asymptotically controllable systems Abstract. Given a globally asymptotically controllable system, we derive from an existence theorem of a semiconcave control-Lyapunov function, the construction of a globally asymptotically stable feedback in the Euler sense. The feedback is rather regular in the case of control systems affine in the control. Abridged English Version In this paper, we study systems of the general form x˙(t) = f(x(t), u(t))(1) where the state x(t) takes values in a Euclidian space Rn, the control u(t) takes values in a given compact set U , and f is locally Lipschitz in (x, u). A special element “0” is distinguished in U , and the state x = 0 of IRn is an equilibrium point, i.

• condition de brockett


• partition pi


• pi-trajectoire


• globalement asymptotiquement


• caratheodory sense


• gas au sens des solutions euler


• lyapunov function