A stochastic approach for computing the domain of attraction without trajectory simulation

Pages: 854 - 863, Issue Special, September 2011

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Péter Koltai - Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3., 85748 Garching bei München, Germany (email)

Abstract: We present an approach for the numerical computation of the domain of attraction of some asymptotically stable set for continuous-time autonomous systems. It is based on a set-oriented approximation of the original dynamical system by a Markov jump process. The domain of attraction is extracted from absorption probabilities of the jump process. The method does not perform any trajectory simulation, integrals of the underlying vector eld on the boundary of partition elements are computed instead.

Keywords:  Domain of attraction, set-oriented method, Frobenius-Perron operator, in nitesimal generator, absorption probability
Mathematics Subject Classification:  Primary: 37M99; Secondary: 65P99

Received: July 2010;      Revised: March 2011;      Published: October 2011.