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.
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Elsevier
Electronic Notes in Theoretical Computer Science
Computational Topology for Systems and Control
Workshop on Reachability Problems
Scientific Computing

Collins, P., & Goldsztejn, A. (2008). The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems. In Electronic Notes in Theoretical Computer Science (Vol. 223, pp. 87–102). Elsevier.