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.

• Type: Journal
• Year: 2008
• Where: AUTOMATICA
• Authors: Ufuk Topcu, Andrew K. Packard, Peter Seiler
• Keywords: AUTOMATICA 2008, Invariant Subsets, Lyapunov Function, Polynomial Vector Fields