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On condition/event systems with discrete state realizations

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Abstract

This paper introduces condition/event (C/E) systems as a class of continuous-time discrete event dynamic systems (DEDS) with two types of discrete-valued input and output signals:condition signals andevent signals. In applications such as discrete control, C/E systems provide an intuitive continuous-time modeling framework amenable to block diagram representation. In this paper we consider C/E systems with discrete state realizations, and study the relationship between continuous-time C/E systems and untimed models of their sequential inputoutput behavior called C/E languages. We show that C/E systems with discrete state realizations are necessarilytime-change invariant (Theorem 3.1), which means the ensemble of admissible continuous-time input-output behaviors is completely characterized by the C/E language for the system (Theorem 4.1). It is also shown that deterministic C/E systems with discrete state realizations are necessarily discrete-time (clocked) systems (Corollary 3.1), and that finite discrete state realizations exist for a C/E system only if its related C/E language has a finite state generator (Theorem 4.2). Finally, we develop equivalent discrete-state realizations for C/E systems resulting from cascade and feedback interconnections. The paper concludes with a discussion of several directions for future research.

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References

  • Bennett, S. 1988.Real-Time Computer Control: An Introduction. Englewood Cliffs, NJ: Prentice Hall.

    Google Scholar 

  • Choueka, Y. 1974. Theories of automata on ω-tapes: A simplified approach.J. Comput. Sys. Sci., 8: 117–141.

    Google Scholar 

  • Eilenberg, S. 1974.Automata, Languages, and Machines. New York: Academic Press.

    Google Scholar 

  • Garey, M.R. and Johnson, D.S. 1979.Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, New York.

    Google Scholar 

  • Glynn, P.W. 1989. A GSMP formalism for discrete event systems.Proc. IEEE, 77: 14–23.

    Google Scholar 

  • Golaszewski, C. H. and Ramadge, P.J. 1987. Control of discrete event processes with forced events.Proc. 26th Conf. on Decision and Control, (Dec.): 247–251, Los Angeles, CA.

  • Heymann, M. 1990. Concurrency and discrete event control.IEEE Control Sys. Mag., 10: 103–112.

    Google Scholar 

  • Inan, K. 1989. Asynchronous dynamical systems.Proc. 28th Conf. on Decision and Control, (Dec.): 1544–1549, Tampa, FL.

  • Krogh, B.H. and Ekberg, G. 1987. Automatic programming of controllers for discrete manufacturing processes.Preprints of the 10th IFAC World Congress, (July): 4: 160–164.

    Google Scholar 

  • Lewis, H.R. and Papadimitriou, C.H. 1981.Elements of the Theory of Computation. Englewood Cliffs, NJ: Prentice Hall.

    Google Scholar 

  • Ramadge, P.J. and Wonham, W.M. 1987. Supervisory control of a class of discrete event processes.SIAM J. Control Optim. 25: 206–230.

    Google Scholar 

  • Ramadge, P.J. and Wonham, W.M. 1987. Modular feedback logic for discrete event systems.SIAM J. Control Optim., 1202–1213.

  • Ramadge, P.J. and Wonham, W.M. 1989. The control of discrete event systems.Proc. IEEE, 77: 81–98.

    Google Scholar 

  • Ramadge, P.J. 1989. Some tractable supervisory control problems for discrete-event systems modeled by Buchi automata.IEEE Trans. Automatic Control, 34: 10–19.

    Google Scholar 

  • Reisig, W. 1982.Petri Nets: An Introduction. Berlin: Springer-Verlag.

    Google Scholar 

  • Rogers, L.C.G. and Williams, D. 1987.Diffusions, Markov Processes, and Martingales, Vol. 2. New York: Wiley.

    Google Scholar 

  • Sreenivas, R.S. 1990.Towards a System Theory for Interconnected Condition/Event Systems. Ph.D. thesis, Carnegie Mellon University.

  • Willems, J.C. 1987.Models for Dynamics. Technical Report, Systems and Control Group, Mathematics Institute, University of Groningen, Groningen, The Netherlands.

    Google Scholar 

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Authors and Affiliations

  1. Division of Applied Sciences, Harvard University, 02138, Cambridge, MA

    R. S. Sreenivas

  2. Department of Electrical and Computer Engineering, Carnegie Mellon University, 15213, Pittsburgh, PA

    B. H. Krogh

Authors
  1. R. S. Sreenivas
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  2. B. H. Krogh
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Please direct correspondence concerning this paper to B.H. Krogh at the above address.

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Sreenivas, R.S., Krogh, B.H. On condition/event systems with discrete state realizations. Discrete Event Dyn Syst 1, 209–236 (1991). https://doi.org/10.1007/BF01805563

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  • DOI: https://doi.org/10.1007/BF01805563

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