Search results for "catégorie log-exp"

Etude asymptotique et transcendance de la fonctionvaleur en contrôle optimal. Catégorie log-exp en géométrie sous-Riemannienne dans le cas Martinet.

2000

The main subject of this work is the study and the role ofabnormal trajectories in optimal control theory.We first recall some fundamental results in optimal control. Thenwe investigate the optimality of abnormal trajectories forsingle-input affine systems with constraint on the control, firstfor the time-optimal problem, and then for any cost, the finaltime being fixed or not.Using such an affine system,we extend this theory to sub-Riemannian systems of rank 2.These results show that, under general conditions, an abnormaltrajectory is \it{isolated} among all solutions of the systemhaving the same limit conditions, and thus is \it{locallyoptimal}, until a first \it{conjugate point} which ca…