Lagrangian manifolds and asymptotically optimal stabilizing feedback control

✍ Scribed by D. McCaffrey; S.P. Banks

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 96 KB
• Volume: 43
• Category: Article
• ISSN: 0167-6911
• DOI: 10.1016/s0167-6911(01)00101-3

✦ Synopsis

Approximations to nonlinear optimal control based on solving a Riccati equation which varies with the state have been put forward in the literature. It is known that such algorithms are asymptotically optimal given large scale asymptotic stability. This paper presents an analysis for estimating the size of the region on which large scale asymptotic stability holds. This analysis is based on a geometrical construction of a viscosity-type Lyapunov function from a stable Lagrangian manifold. This produces a less conservative estimate than existing approaches in the literature by considering regions of state space over which the stable manifold is multi-sheeted rather than just single sheeted.