Summary
This paper presents elements of control-oriented models of hybrid systems with input and output signals. Models can be composed through standard block-diagram interconnections. Transition systems with inputs and outputs are introduced to define the semantics for open-loop hybrid systems. Fixed-point iterations can then used to synthesize logical supervisory controllers. This is illustrated for the problem of designing a supervisor to keep the state of the hybrid system out of a specified set of forbidden states. Recently developed tools for computer-aided modeling, simulation, and verification of hybrid systems are reviewed briefly. The paper concludes with a discussion of open research issues and prospects for applications of the theory to problems of practical interest.
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References
R. Alur, T.A. Henzinger, and P.-H. Ho. Automatic symbolic verification of embedded systems. IEEE Trans. on Software Engineering, 22(3):181–201, Mar 1996.
M. Andersson. OmSim and Omola Tutorial and User’s Manual. Department of Automatic Control, Lund Institute of Technology, Lund, Sweden, March 1995.
E. Asarin, O. Maler, A. Pinueli, and J. Sifakis. Controller synthesis for timed automata. In IFAC Symposium on System Structure and Control, pages 469–474, 1998.
A. Chutinan and B.H. Krogh. Computing polyhedral approximations to flow pipes for dynamic systems. In IEEE Conf. On Decision and Control, Dec. 1998.
A. Chutinan and B.H. Krogh. Verification of polyhedral-invariant hybrid automata using polygonal flow pipe approximations. In J. Van Schuppen, editor, Hybrid Systems: Computation and Control, Lecture Notes in Computer Science. Springer, March 1999.
J.E.R. Cury and B.H. Krogh. Supervisory control of hybrid systems using approximating automata. Journal of the Society of Instrument and Control Engineers (SICE), March 1999.
J.E.R. Cury, B.H. Krogh, and T. Niinomi. Synthesis of supervisory controllers for hybrid systems based on approximating automata. IEEE Trans. on Automatic Control, 43(4):564–569, April 1998. a preliminary version of this paper also appeared in Proc. 34th IEEE CDC, pp. 1461–1466.
C. Daws, A. Olivero, S. Tripakis, and S. Yovine. The tool kronos. In Hybrid Systems III, Verification and Control. Springer Verlag, 1996.
A.R. Deshpande, A. Gollu, and L. Semenzato. Shift Reference Manual. University of California and Berkeley, 1996. PATH Report, PRCS projcet SHIC version 2.17.
D.L. Dill and H. Wong-Toi. Verification of real-time systems by successive over and under approximation. In Computer-Aided Verification, 7th International Conf., pages 409–422, Liege, Belgium, July 1995.
Z. Manna et al. STeP: The Standford temporal prover (educational release), user’s manual. Technical report, Computer Science Department, Standford University, 1995.
S. Sastry, G. Lafferriere, G. J. Pappas. Hybrid systems with finite bisimulations. Technical Report UCB/ERL M98/15, University of California at Berkeley, April 1998.
S. Yovine G. Lafferriere, G. J. Pappas. Decidable hybrid systems. Technical Report UCB/ERL M98/39, University of California at Berkeley, June 1998.
T.A. Henzinger. Hybrid automata with finite bimulations. In Z. Fülöp and F. Gécseg, editors, ICALP 95: Automata, Languages, and Programming, pages 324–335. Springer-Verlag, 1995.
T.A. Henzinger. The theory of hybrid automata. In Proceedings of the 11th Annual Symposium on Logic in Computer Science, pages 278–292. IEEE Computer Society Press, 1996. Invited tutorial.
T.A. Henzinger, P.-H. Ho, and H. Wong-Toi. Algorithmic analysis of nonlinear hybrid systems. IEEE Transactions on Automatic Control, 1988. To appear.
E.K. Kornoushenko. Finite-automation approximation to the behavior of continuous plants. Automation and Remote Control, pages 2068–2074, 1975.
A. Puri, P. Varaiya, and V. Borkar. ε-approximation of differential inclusions. In R. Alur, T. A. Henzinger, and E. D. Sontag, editors, Hybrid Systems III: Verification and Control, pages 362–376. Springer-Verlag, 1996.
O. Stursberg, S. Kowalewski, and S. Engell. Generating timed discrete models of continuous systems. In Proc. 2nd MATHMOD, pages 203–210, Vienna, Austria, Feb. 1997.
Feng Zhao. Automatic Analysis and Synthesis of Controllers for Dynamical Systems Based on Phase-Space Knowledge. PhD thesis, MIT Artificial Intelligence Laboratory, 1992.
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Krogh, B.H., Chutinan, A. (1999). Hybrid Systems: Modeling and Supervisory Control. In: Frank, P.M. (eds) Advances in Control. Springer, London. https://doi.org/10.1007/978-1-4471-0853-5_8
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DOI: https://doi.org/10.1007/978-1-4471-0853-5_8
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1216-7
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