Stability Region Analysis Using Simulations and Sum-of-Squares Programming
Authors
Ufuk Topcu
Andrew Packard
Peter Seiler
Timothy J. Wheeler
Source
Proceedings of the American Control Conference
Date
July 2007.
Length
6 pages.
Abstract
Show Abstract
The problem of computing bounds on the region-of-attraction for systems with polynomial vector fields is considered. Invariant sets of the region-of-attraction are characterized as sublevel sets of Lyapunov functions. Finite dimensional polynomial parameterizations for the Lyapunov functions are used. A methodology utilizing information from simulations to generate Lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed. The suitability of the Lyapunov function candidates are assessed solving linear sum-of-squares optimization problems. Qualified candidates are used to compute provably invariant subsets of the region-of-attraction and to initialize various bilinear search strategies for further optimization. We illustrate the method on several small examples drawn from the literature.
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