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AUTOMATICA
2008

Local stability analysis using simulations and sum-of-squares programming

11 years 5 months ago
Local stability analysis using simulations and sum-of-squares programming
The problem of computing bounds on the region-of-attraction for systems with polynomial vector fields is considered. Invariant subsets of the region-of-attraction are characterized as sublevel sets of Lyapunov functions. Finite dimensional polynomial parameterizations for 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 Lyapunov function candidates are assessed solving linear sum-of-squares optimization problems. Qualified candidates are used to compute invariant subsets of the region-of-attraction and to initialize various bilinear search strategies for further optimization. We illustrate the method on small examples from the literature and several control oriented systems. Key words: Local Stability; Region-of-attraction; Nonlinear dynamics; Sum-of-squares programming; Simulations.
Ufuk Topcu, Andrew K. Packard, Peter Seiler
Added 08 Dec 2010
Updated 08 Dec 2010
Type Journal
Year 2008
Where AUTOMATICA
Authors Ufuk Topcu, Andrew K. Packard, Peter Seiler
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