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Supervision of Discrete-Event Systems: Basics

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Book cover Supervisory Control of Discrete-Event Systems

Part of the book series: Communications and Control Engineering ((CCE))

Abstract

We introduce the concept of controlled discrete-event system, by adjoining to the structure of a language generator a control technology. This amounts to partitioning the set of events into controllable events and uncontrollable, the former being amenable to disablement by an external controller or supervisor. Starting from the fundamental definition of a controllable language, it is shown how to formulate and solve a basic problem of optimal supervision. The formulation is extended to treat event forcing, reconfiguration, mutual state exclusion, and forbidden state subsets. Computation is illustrated using the software package TCT.

The original version of this chapter was revised: Belated corrections have been incorporated. The correction to this chapter is available at https://doi.org/10.1007/978-3-319-77452-7_10

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Change history

  • 29 May 2019

    In the original version of the book, the Chapters 7, 8, 12, 17 and 23 were revised.

Notes

  1. 1.

    In this section we prefer the term  ‘automaton’ for this representation, rather than  ‘generator’, but allow thetransition function to be a partial function.

  2. 2.

    TCT stores the result of condat as a .DAT file, whereas the result of supcon is a .DES file.

  3. 3.

    See also Sect. 3.12.

  4. 4.

    It will be convenient to designate an event by enclosure in \(<\,>\).

  5. 5.

    It will be convenient to designate a state by enclosure in [ ].

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Authors and Affiliations

  1. Systems Control Group, Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada

    W. Murray Wonham

  2. Department of Electrical and Information Engineering, Osaka City University, Osaka, Japan

    Kai Cai

Authors
  1. W. Murray Wonham
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  2. Kai Cai
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Corresponding author

Correspondence to W. Murray Wonham .

Appendix 3.1

Appendix 3.1

EVENT CODING FOR SMALL FACTORY

figure ao

FACTSUP    # states: 12    state set: 0...11    initial state: 0

 marker states: 0

#  transitions: 24

 transition table:

figure ap

FACTSUP printed.

FACTSUP

Control Data are displayed by listing thesupervisor states where disabling occurs, together with the events that must be disabled there.

Control Data:

figure aq

FACTSUP printed.

SIMFTSUP    # states: 3    state set: 0...2    initial state: 0

 marker states: 0

#  transitions: 16

 transition table:

figure ar

SIMFTSUP printed.

SIMFTSUP

Control Data are displayed by listing thesupervisor states where disabling occurs, together with the events that must be disabled there.

Control Data:

figure as

SIMFTSUP printed.

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Wonham, W.M., Cai, K. (2019). Supervision of Discrete-Event Systems: Basics. In: Supervisory Control of Discrete-Event Systems. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-77452-7_3

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