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On Transfinite Hybrid Automata

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Hybrid Systems: Computation and Control (HSCC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3414))

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Abstract

In this paper, we propose a new method to deal with hybrid systems based on the concept of the nonstandard analysis and the Büchi’s transfinite automata. An essential point of the method is a generalization of hybrid automata with hyperfinite iteration of an infinitesimal transition in * ℝ. This nonstandard model of hybrid automata allows discrete but hyperfinite state transition, so that we can describe and reason about the interaction of the continuous and discrete dynamics in the algebraic framework. In this enlarged perspective of the hybrid automata, we discuss about the asymptotic orbit of the dynamics that is peculiar to the hybrid systems such as Zeno.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Ritsumeikan University, Nojihigashi, Kusatsu-city, SIGA, 525-8577, Japan

    Katsunori Nakamura & Akira Fusaoka

Authors
  1. Katsunori Nakamura
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  2. Akira Fusaoka
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Editor information

Editors and Affiliations

  1. Automatic Control Laboratory, ETH Zurich, 8092, Zurich, Switzerland

    Manfred Morari

  2. Computer Engineering and Networks Laboratory, ETH Zurich, Switzerland

    Lothar Thiele

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Nakamura, K., Fusaoka, A. (2005). On Transfinite Hybrid Automata. In: Morari, M., Thiele, L. (eds) Hybrid Systems: Computation and Control. HSCC 2005. Lecture Notes in Computer Science, vol 3414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31954-2_32

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  • DOI: https://doi.org/10.1007/978-3-540-31954-2_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25108-8

  • Online ISBN: 978-3-540-31954-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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