Stability Region Analysis Using Simulations and Sum-of-Squares Programming
Topcu, U.
Packard, A.
Seiler, P.
Wheeler, T.
Dept. of Mech. Eng., Univ. of California, Berkeley, CA;
This paper appears in: American Control Conference, 2007. ACC '07
Publication Date: 9-13 July 2007
On page(s): 6009-6014
Location: New York, NY,
ISSN: 0743-1619
ISBN: 1-4244-0988-8
INSPEC Accession Number: 9946394
Digital Object Identifier: 10.1109/ACC.2007.4283013
Current Version Published: 2007-07-30
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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