Zonotope/hyperplane intersection for hybrid systems reachability analysis

Abstract : In this paper, we are concerned with the problem of computing the reachable sets of hybrid systems with (possibly high dimensional) linear continuous dynamics and guards defined by switching hyperplanes. For the reachability analysis of the continuous dynamics, we use an efficient approximation algorithm based on zonotopes. In order to use this technique for the analysis of hybrid systems, we must also deal with the discrete transitions in a satisfactory (i.e. scalable and accurate) way. For that purpose, we need to approximate the intersection of the continuous reachable sets with the guards enabling the discrete transitions. The main contribution of this paper is a novel algorithm for computing efficiently a tight over-approximation of the intersection of (possibly high-order) zonotopes with a hyperplane. We show the accuracy and the scalability of our approach by considering two examples of reachability analysis of hybrid systems.
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https://hal.archives-ouvertes.fr/hal-00306993
Contributor : Antoine Girard <>
Submitted on : Monday, July 28, 2008 - 5:03:00 PM
Last modification on : Thursday, July 4, 2019 - 9:54:02 AM

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Antoine Girard, Colas Le Guernic. Zonotope/hyperplane intersection for hybrid systems reachability analysis. HSCC 2008 - Hybrid Systems: Computation and Control, Apr 2008, St. Louis, MO, United States. pp.215-228, ⟨10.1007/978-3-540-78929-1_16⟩. ⟨hal-00306993⟩

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