The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems

Authors:
Pieter Collins;Alexandre Goldsztejn
Affiliations:
Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands;CNRS, LINA, UMR 6241, Nantes, France
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2008

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Abstract

This paper introduces a new algorithm dedicated to the rigorous reachability analysis of nonlinear dynamical systems. The algorithm is initially presented in the context of discrete time dynamical systems, and then extended to continuous time dynamical systems driven by ODEs. In continuous time, this algorithm is called the Reach and Evolve algorithm. The Reach and Evolve algorithm is based on interval analysis and a rigorous discretization of space and time. Promising numerical experiments are presented.