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Choice of Directions for the Approximation of Reachable Sets for Hybrid Systems

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Computer Aided Systems Theory – EUROCAST 2011 (EUROCAST 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6927))

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Abstract

In this paper we propose an approach to over-approximate the reachable set (with bounded time and number of transitions) of a hybrid system by a finite set of polytopes. The constraints of the polytope are determined by a direction choice method. For the hybrid systems whose (1) continuous dynamics are linear, (2) invariants and guards are defined by linear inequalities, and (3) variable resets are expressed by invertible affine maps, we show that the over-approximations can be computed in polynomial time, and the overestimation can be arbitrarily reduced by decreasing the discretization time step if the continuous dynamics are all deterministic. Some experimental results are also presented to show the effectiveness of our approach.

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Author information

Authors and Affiliations

  1. RWTH Aachen University, Germany

    Xin Chen & Erika Ábrahám

Authors
  1. Xin Chen
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  2. Erika Ábrahám
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Editor information

Editors and Affiliations

  1. Instituto Universitario de Ciencias y Tecnologías Cibernéticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira, 35017, Las Palmas de Gran Canaria, Spain

    Roberto Moreno-Díaz  & Alexis Quesada-Arencibia  & 

  2. Institute of Systems Science, Johannes Kepler University Linz, Altenbergerstrasse 69, 4040, Linz, Austria

    Franz Pichler

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Chen, X., Ábrahám, E. (2012). Choice of Directions for the Approximation of Reachable Sets for Hybrid Systems. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2011. EUROCAST 2011. Lecture Notes in Computer Science, vol 6927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27549-4_69

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  • DOI: https://doi.org/10.1007/978-3-642-27549-4_69

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27548-7

  • Online ISBN: 978-3-642-27549-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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