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Zonotope/Hyperplane Intersection for Hybrid Systems Reachability Analysis

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Hybrid Systems: Computation and Control (HSCC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4981))

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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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Magnus Egerstedt Bud Mishra

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Girard, A., Le Guernic, C. (2008). Zonotope/Hyperplane Intersection for Hybrid Systems Reachability Analysis. In: Egerstedt, M., Mishra, B. (eds) Hybrid Systems: Computation and Control. HSCC 2008. Lecture Notes in Computer Science, vol 4981. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78929-1_16

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  • DOI: https://doi.org/10.1007/978-3-540-78929-1_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78928-4

  • Online ISBN: 978-3-540-78929-1

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