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Approximate Reachability for Linear Systems

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Book cover Hybrid Systems: Computation and Control (HSCC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2623))

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Abstract

We describe new techniques to construct, and subsequently refine, over-approximations of the reachability sets for linear dynamical systems. Our approach extracts information from real eigenvectors and more generally, from certain vectors in the primary decomposition, to generate suitable invariants of the system and can be used in conjunction with other reachability computation methods. We also describe experimental results from using this technique inside the qualitative abstraction tool [18], where it helps to generate refined abstractions of hybrid systems with linear continuous dynamics. We illustrate this on a collision-avoidance example from automobile cruise control problem, which was handled completely automatically by our tool.

Research supported in part by DARPA under the MoBIES program administered by AFRL under contract F33615-00-C-1700 and NASA Langley Research Center contract NAS1-00108 to Rannoch Corporation.

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Author information

Authors and Affiliations

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

    Ashish Tiwari

Authors
  1. Ashish Tiwari
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Editor information

Editors and Affiliations

  1. CNRS-VERIMAG, 2 avenue de Vignate, 38610, Gières, France

    Oded Maler

  2. Weizmann Institute of Science, Rehovot, 76100, Israel

    Amir Pnueli

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© 2003 Springer-Verlag Berlin Heidelberg

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Tiwari, A. (2003). Approximate Reachability for Linear Systems. In: Maler, O., Pnueli, A. (eds) Hybrid Systems: Computation and Control. HSCC 2003. Lecture Notes in Computer Science, vol 2623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36580-X_37

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  • DOI: https://doi.org/10.1007/3-540-36580-X_37

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00913-9

  • Online ISBN: 978-3-540-36580-8

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