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Reachability Analysis of Multi-affine Systems

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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

We present a technique for reachability analysis of continuous multi-affine systems based on rectangular partitions. The method is iterative. At each step, finer partitions and larger discrete quotients are produced. We exploit some interesting convexity properties of multi-affine functions on rectangles to show that the construction of the discrete quotient at each step requires only the evaluation of the vector field at the set of all vertices of all rectangles in the partition and finding the roots of a finite set of scalar affine functions. The methodology promises to be easily extendable to rectangular hybrid automata with multi-affine vector fields and is expected to find important applications in analysis of biological networks and robot control.

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Author information

Authors and Affiliations

  1. Center for Information and Systems Engineering, Boston University, 15 Saint Mary’s Street, Brookline, MA, 02446, USA

    Marius Kloetzer & Calin Belta

Authors
  1. Marius Kloetzer
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  2. Calin Belta
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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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© 2006 Springer-Verlag Berlin Heidelberg

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Kloetzer, M., Belta, C. (2006). Reachability Analysis of Multi-affine 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_27

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  • DOI: https://doi.org/10.1007/11730637_27

  • 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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