Synthesizing controllers for nonlinear hybrid systems

  • Claire Tomlin
  • John Lygeros
  • Shankar Sastry
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1386)

Abstract

Motivated by an example from aircraft conflict resolution we seek a methodology for synthesizing controllers for nonlinear hybrid automata. We first show how game theoretic methodologies developed for this purpose for finite automata and continuous systems can be cast in a unified framework. We then present a conceptual algorithm for extending them to the hybrid setting. We conclude with a discussion of computational issues.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Church, “Logic, arithmetic, and automata,” in Proceedings of the International Congress of Mathematicians, pp. 23–35, 1962.Google Scholar
  2. 2.
    J. von Neumann and O. Morgenstern, Theory of games and economic behavior. Princeton university press, 1947.Google Scholar
  3. 3.
    J. R. Büchi and L. H. Landweber, “Solving sequential conditions by finite-state operators,” in Proceedings of the American Mathematical Society, pp. 295–311, 1969.Google Scholar
  4. 4.
    M. O. Rabin, “Automata on infinite objects and Church's problem,” in Regional Conference Series in Mathematics, 1972.Google Scholar
  5. 5.
    A. Puri, Theory of Hybrid Systems and Discrete Event Systems. PhD thesis, Department of Electrical Engineering, University of California, Berkeley, California, 1995.Google Scholar
  6. 6.
    W. Thomas, “Automata on infinite objects,” in Formal Models and Semantics, volume B of Handbook of Theoretical Computer Science, Elsevier Science, 1990.Google Scholar
  7. 7.
    W. Thomas, “On the synthesis of strategies in infinite games,” in Proceedings of STACS 95, Volume 900 of LNCS (E. W. Mayr and C. Puech, eds.), pp. 1–13, Munich: Springer Verlag, 1995.Google Scholar
  8. 8.
    O. Maler, A. Pnueli, and J. Sifakis, “On the synthesis of discrete controllers for timed systems,” in STACS 95: Theoretical Aspects of Computer Science (E. W. Mayr and C. Puech, eds.), Lecture Notes in Computer Science 900, pp. 229–242, Munich: Springer Verlag, 1995.Google Scholar
  9. 9.
    E. Asarin, O. Maler, and A. Pnueli, “Symbolic controller synthesis for discrete and timed systems,” in Proceedings of Hybrid Systems II, Volume 999 of LNCS (P. Antsaklis, W. Kohn, A. Nerode, and S. Sastry, eds.), Cambridge: Springer Verlag, 1995.Google Scholar
  10. 10.
    H. Wong-Toi, “The synthesis of controllers for linear hybrid automata,” in Proceedings of the IEEE Conference on Decision and Control, (San Diego, CA), 1997.Google Scholar
  11. 11.
    W. M. Wonham, Linear Multivariable Control: a geometric approach. Springer Verlag, 1979.Google Scholar
  12. 12.
    A. Deshpande and P. Varaiya, “Viable control of hybrid systems,” in Hybrid Systems II (P. Antsaklis, W. Kohn, A. Nerode, and S. Sastry, eds.), Lecture Notes in Computer Science 999, pp. 128–147, Berlin: Springer Verlag, 1995.Google Scholar
  13. 13.
    R. Isaacs, Differential Games. John Wiley, 1967.Google Scholar
  14. 14.
    T. Baar and G. J. Olsder, Dynamic Non-cooperative Game Theory Academic Press, seconded., 1995.Google Scholar
  15. 15.
    C. Tomlin, G. Pappas, and S. Sastry, “Conflict resolution for air traffic management: A case study in multi-agent hybrid systems,” tech. rep., UCB/ERL M97/33, Electronics Research Laboratory, University of California, Berkeley, 1997. To appear in the IEEE Transactions on Automatic Control.Google Scholar
  16. 16.
    J. Lygeros, D. N. Godbole, and S. Sastry, “A verified hybrid controller for automated vehicles,” Tech. Rep. UCB-ITS-PRR-97-9, Institute of Transportation Studies, University of California, Berkeley, 1997. To appear in the IEEE Transactions on Automatic Control, Special Issue on Hybrid Systems, April 1998.Google Scholar
  17. 17.
    A. E. Bryson and Y.-C. Ho, Applied Optimal Control. Waltham: Blaisdell Publishing Company, 1969.Google Scholar
  18. 18.
    J. A. Sethian, “Theory, algorithms, and applications of level set methods for propagating interfaces,” tech. rep., Center for Pure and Applied Mathematics (PAM-651), University of California, Berkeley, 1995.Google Scholar
  19. 19.
    J. M. Berg, A. Yezzi, and A. R. Tannenbaum, “Phase transitions, curve evolution, and the control of semiconductor manufacturing processes,” in Proceedings of the IEEE Conference on Decision and Control, (Kobe), pp. 3376–3381, 1996.Google Scholar
  20. 20.
    uP. L. Lions, Generalized Solutions of Hamilton-Jacobi Equations.London: Pittman, 1982.Google Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Claire Tomlin
    • 1
  • John Lygeros
    • 1
  • Shankar Sastry
    • 1
  1. 1.Department of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkelev

Personalised recommendations