Stability region analysis using simulations and sum-of-squares programming

Ufuk Topcu; Andrew Packard; Peter Seiler; Timothy Wheeler

doi:10.1109/ACC.2007.4283013

Stability region analysis using simulations and sum-of-squares programming

Ufuk Topcu, Andrew Packard, Peter Seiler, Timothy Wheeler

Aerospace Engineering and Mechanics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

36 Scopus citations

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.

Original language	English (US)
Title of host publication	Proceedings of the 2007 American Control Conference, ACC
Pages	6009-6014
Number of pages	6
DOIs	https://doi.org/10.1109/ACC.2007.4283013
State	Published - Dec 1 2007
Event	2007 American Control Conference, ACC - New York, NY, United States Duration: Jul 9 2007 → Jul 13 2007

Other

Other	2007 American Control Conference, ACC
Country	United States
City	New York, NY
Period	7/9/07 → 7/13/07

Access

10.1109/ACC.2007.4283013

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title = "Stability region analysis using simulations and sum-of-squares programming",

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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AU - Topcu, Ufuk

AU - Packard, Andrew

AU - Seiler, Peter

AU - Wheeler, Timothy

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N2 - 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.

AB - 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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