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Computation of Discrete Abstractions of Arbitrary Memory Span for Nonlinear Sampled Systems

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Hybrid Systems: Computation and Control (HSCC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5469))

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Abstract

In this paper, we present a new method for computing discrete abstractions of arbitrary memory span for nonlinear sampled systems with quantized output. In our method, abstractions are represented by collections of conservative approximations of reachable sets by polyhedra, which in turn are represented by collections of half-spaces. Important features of our approach are that half-spaces are shared among polyhedra, and that the determination of each half-space requires the solution of a single initial value problem in an ordinary differential equation over a single sampling interval only. Apart from these numerical integrations, the only nontrivial operation to be performed repeatedly is to decide whether a given polyhedron is empty. In particular, in contrast to previous approaches, there are no intermediate bloating steps, and convex hulls are never computed. Our method heavily relies on convexity of reachable sets and applies to any sufficiently smooth system if either the sampling period, or the system of level sets of the quantizer can be chosen freely. In particular, it is not required that the system to be abstracted have any stability properties.

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Authors and Affiliations

  1. Fakultät Elektrotechnik und Informatik, Heinrich-Hertz-Lehrstuhl für Mobilkommunikation HFT 6, Technische Universität Berlin, Einsteinufer 25, D-10587, Berlin, Germany

    Gunther Reißig

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  1. Gunther Reißig
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Editors and Affiliations

  1. Department of Computer Science, University of California, 4531E Boelter Hall, CA 90095, Los Angeles, USA

    Rupak Majumdar

  2. Department of Electrical Engineering, University of California, 66-147F Engineering, IV Building, CA 90095-1594, Los Angeles, USA

    Paulo Tabuada

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Reißig, G. (2009). Computation of Discrete Abstractions of Arbitrary Memory Span for Nonlinear Sampled Systems. In: Majumdar, R., Tabuada, P. (eds) Hybrid Systems: Computation and Control. HSCC 2009. Lecture Notes in Computer Science, vol 5469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00602-9_22

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  • DOI: https://doi.org/10.1007/978-3-642-00602-9_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00601-2

  • Online ISBN: 978-3-642-00602-9

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