A Geometric Approach to Bisimulation and Verification of Hybrid Systems

  • Mireille Broucke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1569)


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.


Model Check Hybrid System Geometric Approach Parallel Composition Integral Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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.CrossRefGoogle Scholar
  2. 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.CrossRefMathSciNetGoogle Scholar
  3. 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. 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.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    T. Henzinger. Hybrid automata with finite bisimulations. In “Proc. 22nd ICALP: Automata, Languages and Programming, LNCS 944, pp. 324–335, Springer-Verlag, 1995.Google Scholar
  6. 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.CrossRefGoogle Scholar
  7. 7.
    H.B. Lawson. The Quantitative theory of foliations. Regional Conference Series in Mathematics, no. 27. American Mathematical Society, Providence, 1977.Google Scholar
  8. 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.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    J. Palis and W. de Melo. Geometric Theory of Dynamical Systems: an Introduction. Springer-Verlag, New York, 1982.zbMATHGoogle Scholar
  10. 10.
    W. Sluis. Absolute Equivalence and its Applications to Control Theory. Ph.D. thesis, University of Waterloo, 1992.Google Scholar
  11. 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.CrossRefGoogle Scholar
  12. 12.
    F. Warner. Foundations of DifferentialManifolds and Lie Groups. Springer-Verlag, New York, 1983.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Mireille Broucke
    • 1
  1. 1.Deparment of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkeleyUSA

Personalised recommendations