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Control theory, modal logic, and games

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Hybrid Systems IV (HS 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1273))

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Abstract

We consider a class of discrete systems, with specifications stated in a certain modal temporal language (chosen for simplicity). We show that if the regulator can in some way guarantee satisfaction of a specification, then it can do so acting as a deterministic finite automaton, and we can effectively find an appropriate automaton, or determine that there is none. Our result is not really new. It (and similar results for more expressive languages) can be obtained easily from a result of Landweber and Bfichi on “regular” games, together with the fact that our language gives rise to games of this sort (see the excellent surveys [T] and [E]). We use a result of Gurevich and Harrington [G-H] to show the existence of appropriate automata. The actual construction is explicit. The set of states is determined through elementary considerations of which partial records might be useful to the regulator.

The authors are grateful to Jenny Davoren, Yuri Gurevich, Michael Lemmon, and Anil Nerode.

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Authors and Affiliations

  1. University of Notre Dame, USA

    Julia. F. Knight

  2. University of Chicago, USA

    Brian Luense

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  1. Julia. F. Knight
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  2. Brian Luense
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Panos Antsaklis Wolf Kohn Anil Nerode Shankar Sastry

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© 1997 Springer-Verlag Berlin Heidelberg

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Knight, J.F., Luense, B. (1997). Control theory, modal logic, and games. In: Antsaklis, P., Kohn, W., Nerode, A., Sastry, S. (eds) Hybrid Systems IV. HS 1996. Lecture Notes in Computer Science, vol 1273. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031560

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  • DOI: https://doi.org/10.1007/BFb0031560

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  • Print ISBN: 978-3-540-63358-7

  • Online ISBN: 978-3-540-69523-3

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