Comparing timed and hybrid automata as approximations of continuous systems

  • Olaf Stursberg
  • Stefan Kowalewski
  • Ingo Hoffmann
  • Jörg Preußig
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1273)


We describe two approaches to derive Timed and Linear Hybrid Automata from continuous models given as systems of ordinary differential equations. A semiquantitative modeling method is applied which yields a qualitative description of the system dynamics and quantitative bounds for the residence times in the discrete states or the state variable derivatives. We discuss the problem of spurious trajectories and illustrate the two aproaches by means of a simple process engineering example. Results of a reachability analysis obtained with the tool HyTech are presented.


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  1. 1.
    R. Alur, C. Courcoubetis, N. Halbwachs, T. A. Henzinger, P.-H. Ho, X. Nicollin, A. Olivero, J. Sifakis and S. Yovine, “The Algorithmic Analysis of Hybrid Systems”, Theoretical Computer Science, Vol. 138, pp. 3–34, 1995.Google Scholar
  2. 2.
    R. Alur and D. L. Dill, “A Theory of Timed Automata”, Theoretical Computer Science, Vol. 126, pp. 183–235, 1994.Google Scholar
  3. 3.
    T. Heckenthaler and S. Engell, “Approximately Time-Optimal Fuzzy Control of a Two-Tank System”, IEEE Control Systems, Vol. 14, No. 3, pp. 24–30, 1994.Google Scholar
  4. 4.
    T. A. Henzinger and P.-H. Ho, “HyTech: The Cornell HYbrid TECHnology Tool”, Basic Research in Computer Science, Proc. Workshop on Tools and Algorithms for the Construction and Analysis of Systems, Aarhus, Denmark, May 1995.Google Scholar
  5. 5.
    T. A. Henzinger and H. Wong-Toi, “Linear Phase-portrait Approximations for Nonlinear Hybrid Systems”, Hybrid Systems III: Verification and Control, LNCS 1066, Springer, pp. 377–388, 1996.Google Scholar
  6. 6.
    S. Kowalewski, R. Gesthuisen and V. Roßmann “Model-based Verification of Batch Process Control Software”, Proc. IEEE Conf. on Systems, Man and Cybernetics, San Antonio, USA, pp. 331–336, 1994.Google Scholar
  7. 7.
    M. M. Kokar, “On Consistent Symbolic Representations of General Dynamic Systems”, IEEE Trans. Systems, Man, and Cybernetics, Vol. 25, No. 8, August 1995.Google Scholar
  8. 8.
    S. Kowalewski and J. Preußig, “Timed/Condition/Event Sytems: A Framework for Modular Discrete Models of Chemical Plants and Verification of Their Real-Time Discrete Control”, in Tools and Algorithms for the Construction and Analysis of Systems, LNCS 1055, Springer, 1996.Google Scholar
  9. 9.
    B. Kuipers, “Qualitative Simulation”, Artificial Intelligence, Vol. 29, pp. 289–338, 1986.Google Scholar
  10. 10.
    J. Lunze, “Qualitative Modelling of Linear Dynamical Systems with Quantized State Measurements”, Automatica, Vol. 30, No. 3, pp. 417–431, 1994.Google Scholar
  11. 11.
    I. Moon, G. J. Powers, J. R. Burch and E. M. Clarke, “Automatic Verification of Sequential Control Systems Using Temporal Logic”, AICHE Journal, Vol. 38, No. 1, pp. 67–75, 1992.Google Scholar
  12. 12.
    X. Nicollin, J. Sifakis and S. Yovine, “Compiling Real-Time Specifications into Extended Automata”, IEEE Trans. on Software Eng., 18 (9), pp. 794–804, 1992.Google Scholar
  13. 13.
    T. Niinomi, B. H. Krogh and J. E. R. Cury, “Synthesis of Supervisory Controllers for Hybrid Systems based on Approximating Automata”, Conf. on Decision and Control, New Orleans, 1995.Google Scholar
  14. 14.
    H. A. Preisig and J. Renz, “Synthesis of a Supervisory Controller from First Principles”, Annual AICHE Meeting, Miami, November 1992.Google Scholar
  15. 15.
    J. Raisch and S. O'Young, “A DES Approach to Control of Hybrid Dynamical Syytems”, Workshop on Analysis and Design of Event-driven Operations in Process-Systems (ADEDOPS), London, 1995.Google Scholar
  16. 16.
    J. Sifakis, “Use of Petri nets for performance evaluation”, In H. Beilner and E. Gelenebe (editors), Measuring, modelling and evaluating computer systems, pp. 75–93. North-Holland, 1977.Google Scholar
  17. 17.
    J. A. Stiver and P. J. Antsaklis, “State Space Partitioning for Hybrid Control Systems”, Proc. of the American Control Conference, San Francisco, California, pp. 2303–2304, June 1993.Google Scholar
  18. 18.
    O. Stursberg, S. Kowalewski and S. Engell, “Generating Timed Discrete Models of Continuous Systems”, 2nd IMACS Symposium on Mathematical Modelling (MATHMOD'97), Vienna, Austria, Feb. 5–7th, 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Olaf Stursberg
    • 1
  • Stefan Kowalewski
    • 1
  • Ingo Hoffmann
    • 1
  • Jörg Preußig
    • 1
  1. 1.Process Control Group (CT-AST), Department of Chemical EngineeringUniversity of DortmundGermany

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