Skip to main content
SpringerLink
Log in

On supremal languages of classes of sublanguages that arise in supervisor synthesis problems with partial observation

  • Published:
Mathematics of Control, Signals and Systems Aims and scope Submit manuscript

Abstract

This paper characterizes the class of closed and (M, N)-recognizable languages in terms of certain structural aspects of relevant automata. This characterization leads to algorithms that effectively compute the supremal (M, N)-recognizable sublanguage of a given language. One of these algorithms is used, in an alternating manner with an algorithm which yields the supremal (∑u, N)-invariant resulting algorithm is proved. An example illustrates the use of these algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Cieslak, C. Desclaux, A. Fawaz, and P. Varaiya, Supervisory control of discrete-event processes with partial observations,IEEE Trans. Automat. Control,33 (1988), 249–260.

    Article  Google Scholar 

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

    MATH  Google Scholar 

  3. J.E. Hopcroft and J.D. Ullman,Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, MA, 1979.

    MATH  Google Scholar 

  4. F. Lin and W. M. Wonham, On Observability of Discrete-Event Systems, Systems Control Group Report No. 8701, Department of Electrical Engineering University of Toronto, 1987.

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

    Article  MathSciNet  Google Scholar 

  6. R. Smedinga, Control of Discrete Events, Preprint, University of Groningen, Groningen, 1987.

  7. J.N. Tsitsiklis, On the control of discrete-event dynamical systems,Proceedings of the 26th IEEE Conference on Decision and Control, Los Angeles, 1987, pp. 419–422.

  8. W.M. Wonham and P.J. Ramadge, On the supremal controllable sublanguage of a given language,SIAM J. Control Optim.,25 (1987), 637–659.

    Article  MathSciNet  Google Scholar 

  9. W.M. Wonham and P.J. Ramadge, Modular supervisory control of discrete-event systems,Math. Control Signals Systems,1 (1988), 13–30.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Texas at Austin, 78712-1084, Texas, Austin, U.S.A.

    Hangju Cho & Steven I. Marcus

Authors
  1. Hangju Cho
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Steven I. Marcus
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported in part by the Air Force Office of Scientific Research under Grant No. AFOSR-86-0029, in part by the National Science Foundation under Grant No. ECS-8412100, and in part by the DoD Joint Services Electronics Program through the Air Force Office of Scientific Research (AFSC) Contract No. F49620-86-C-0045

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cho, H., Marcus, S.I. On supremal languages of classes of sublanguages that arise in supervisor synthesis problems with partial observation. Math. Control Signal Systems 2, 47–69 (1989). https://doi.org/10.1007/BF02551361

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02551361

Key words

Search

Navigation