Brief paper: Local stability analysis using simulations and sum-of-squares programming

Authors:
Ufuk Topcu;Andrew Packard;Peter Seiler
Affiliations:
Department of Mechanical Engineering, University of California, Berkeley, 94720-1740, USA;Department of Mechanical Engineering, University of California, Berkeley, 94720-1740, USA;Honeywell Technology Center, Minneapolis, MN, 55418, USA
Venue:
Automatica (Journal of IFAC)
Year:
2008

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Abstract

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 parametrizations 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 is 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.