Lagrangian manifolds and asymptotically optimal stabilizing feedback control

Approximations to nonlinear optimal control based on solving a Riccati equa tion which varies with the state have been put forward in the literature. I t is known that such algorithms are asymptotically optimal given large scal e asymptotic stability. This paper presents an analysis for estimating the size of the region on which large scale asymptotic stability holds. This an alysis is based on a geometrical construction of a viscosity-type Lyapunov function from a stable Lagrangian manifold. This produces a less conservati ve estimate than existing approaches in the literature by considering regio ns of state space over which the stable manifold is multi-sheeted rather th an just single sheeted. (C) 2001 Elsevier Science B.V. All rights reserved.