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A Geometric Approach to Bisimulation and Verification of Hybrid Systems

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Hybrid Systems: Computation and Control (HSCC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1569))

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Abstract

An approximate verification method for hybrid systems in which sets of the automaton are over-approximated, while leaving the vector fields intact, is presented. The method is based on a geometricallyinspired approach, using tangential and transversal foliations, to obtain bisimulations. Exterior differential systems provide a natural setting to obtain an analytical representation of the bisimulation, and to obtain the bisimulation under parallel composition. We define the symbolic execution theory and give applications to coordinated aircraft and robots.

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References

  1. R. Alur and D.L. Dill. Automata for modeling real-time systems. In “Proc. 17th ICALP: Automata, Languages and Programming, LNCS 443, Springer-Verlag, 1990.

    Google Scholar 

  2. P. Caines and Y. Wei. The hierarchical lattices of a finite machine. Systems and Control Letters, vol. 25, no. 4, pp. 257–263, July, 1995.

    Article  MathSciNet  Google Scholar 

  3. P. Caines and Y. Wei. On dynamically consistent hybrid systems. In P. Antsaklis, W. Kohn, A. Nerode, eds., Hybrid Systems II, pp. 86–105, Springer-Verlag, 1995.

    Google Scholar 

  4. L.O. Chua, M. Komuro, and T. Matsumoto. The double scroll family-part I: rigorous proof of chaos. IEEE Transactions on Circuits and systems vol. 33, no. 11, pp. 1072–1097, November, 1986.

    Article  MathSciNet  Google Scholar 

  5. T. Henzinger. Hybrid automata with finite bisimulations. In “Proc. 22nd ICALP: Automata, Languages and Programming, LNCS 944, pp. 324–335, Springer-Verlag, 1995.

    Chapter  Google Scholar 

  6. T. Henzinger. The theory of hybrid automata. In Proc. 11th IEEE Symposium on Logic in Computer Science, pp. 278–292, New Brunswick, NJ, 1996.

    Chapter  Google Scholar 

  7. H.B. Lawson. The Quantitative theory of foliations. Regional Conference Series in Mathematics, no. 27. American Mathematical Society, Providence, 1977.

    Google Scholar 

  8. R. Murray and S. Sastry. Nonholonomic motion planning: steering using sinusoids. IEEE Transactions on Automatic Control, vol.38, no.5, pp. 700–716, May, 1993.

    Article  MathSciNet  Google Scholar 

  9. J. Palis and W. de Melo. Geometric Theory of Dynamical Systems: an Introduction. Springer-Verlag, New York, 1982.

    Book  Google Scholar 

  10. W. Sluis. Absolute Equivalence and its Applications to Control Theory. Ph.D. thesis, University of Waterloo, 1992.

    Google Scholar 

  11. C. Tomlin, G. Pappas, J. Lygeros, D. Godbole, and S. Sastry. Hybrid Control Models of Next Generation Air Traffic Management. In P. Antsaklis, W. Kohn, A. Nerode, and S. Sastry, eds., Hybrid Systems IV, LNCS 1273, pp. 378–404, Springer-Verlag, 1997.

    Chapter  Google Scholar 

  12. F. Warner. Foundations of DifferentialManifolds and Lie Groups. Springer-Verlag, New York, 1983.

    Book  Google Scholar 

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Author information

Authors and Affiliations

  1. Deparment of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, 94720, USA

    Mireille Broucke

Authors
  1. Mireille Broucke
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Editor information

Editors and Affiliations

  1. Computing Science Institute, University of Nijmegen, P.O. Box 9010, 6500, GL, Nijmegen, The Netherlands

    Frits W. Vaandrager

  2. CWI, P.O. Box 94079, 1090, GB, Amsterdam, The Netherlands

    Jan H. van Schuppen

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© 1999 Springer-Verlag Berlin Heidelberg

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Broucke, M. (1999). A Geometric Approach to Bisimulation and Verification of Hybrid Systems. In: Vaandrager, F.W., van Schuppen, J.H. (eds) Hybrid Systems: Computation and Control. HSCC 1999. Lecture Notes in Computer Science, vol 1569. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48983-5_9

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  • DOI: https://doi.org/10.1007/3-540-48983-5_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65734-7

  • Online ISBN: 978-3-540-48983-2

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