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Computational Methods for Reachability Analysis of Stochastic Hybrid Systems

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Book cover Hybrid Systems: Computation and Control (HSCC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3927))

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Abstract

Stochastic hybrid system models can be used to analyze and design complex embedded systems that operate in the presence of uncertainty and variability. Verification of reachability properties for such systems is a critical problem. Developing algorithms for reachability analysis is challenging because of the interaction between the discrete and continuous stochastic dynamics. In this paper, we propose a probabilistic method for reachability analysis based on discrete approximations. The contribution of the paper is twofold. First, we show that reachability can be characterized as a viscosity solution of a system of coupled Hamilton-Jacobi-Bellman equations. Second, we present a numerical method for computing the solution based on discrete approximations and we show that this solution converges to the one for the original system as the discretization becomes finer. Finally, we illustrate the approach with a navigation benchmark that has been proposed for hybrid system verification.

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Author information

Authors and Affiliations

  1. Institute for Software Integrated Systems, Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN, 37235, USA

    Xenofon Koutsoukos & Derek Riley

Authors
  1. Xenofon Koutsoukos
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  2. Derek Riley
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Editor information

Editors and Affiliations

  1. Center for Control, Dynamical Systems and Computation, University of California, 93106, Santa Barbara, CA, USA

    João P. Hespanha

  2. SRI International, 333 Ravenswood Ave, Menlo Park, CA, USA

    Ashish Tiwari

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Koutsoukos, X., Riley, D. (2006). Computational Methods for Reachability Analysis of Stochastic Hybrid Systems. In: Hespanha, J.P., Tiwari, A. (eds) Hybrid Systems: Computation and Control. HSCC 2006. Lecture Notes in Computer Science, vol 3927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11730637_29

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  • DOI: https://doi.org/10.1007/11730637_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33170-4

  • Online ISBN: 978-3-540-33171-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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