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Rectangular Hybrid Games

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Book cover CONCUR’99 Concurrency Theory (CONCUR 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1664))

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Abstract

In order to study control problems for hybrid systems, we generalize hybrid automata to hybrid games —say, controller vs. plant. If we specify the continuous dynamics by constant lower and upper bounds, we obtain rectangular games. We show that for rectangular games with objectives expressed in Ltl (linear temporal logic), the winning states for each player can be computed, and winning strategies can be synthesized. Our result is sharp, as already reachability is undecidable for generalizations of rectangular systems, and optimal —singly exponential in the size of the game structure and doubly exponential in the size of the Ltl objective. Our proof systematically generalizes the theory of hybrid systems from automata (single-player structures) [9] to games (multi-player structures): we show that the successively more general infinite-state classes of timed, 2D rectangular, and rectangular games induce successively weaker, but still finite, quotient structures called game bisimilarity, game similarity, and game trace equivalence. These quotients can be used, in particular, to solve the Ltl control problem.

This research was supported in part by the NSF CAREER award CCR-9501708, by the NSF grant CCR-9504469, by the DARPA (NASA Ames) grant NAG2-1214, by the DARPA (Wright-Patterson AFB) grant F33615-98-C-3614, and by the ARO MURI grant DAAH-04-96-1-0341.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, 94720-1770, USA

    Thomas A. Henzinger, Benjamin Horowitz & Rupak Majumdar

  2. Max-Planck Institute for Computer Science, Im Stadtwald, 66123, Saarbrücken, Germany

    Thomas A. Henzinger, Benjamin Horowitz & Rupak Majumdar

Authors
  1. Thomas A. Henzinger
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  2. Benjamin Horowitz
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  3. Rupak Majumdar
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Editor information

Editors and Affiliations

  1. Department of Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Jos C. M. Baeten  & Sjouke Mauw  & 

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Henzinger, T.A., Horowitz, B., Majumdar, R. (1999). Rectangular Hybrid Games. In: Baeten, J.C.M., Mauw, S. (eds) CONCUR’99 Concurrency Theory. CONCUR 1999. Lecture Notes in Computer Science, vol 1664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48320-9_23

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  • DOI: https://doi.org/10.1007/3-540-48320-9_23

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  • Print ISBN: 978-3-540-66425-3

  • Online ISBN: 978-3-540-48320-5

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