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.
In this section we prefer the term ‘automaton’ for this representation, rather than ‘generator’, but allow thetransition function to be a partial function.
- 2.
TCT stores the result of condat as a .DAT file, whereas the result of supcon is a .DES file.
- 3.
See also Sect. 3.12.
- 4.
It will be convenient to designate an event by enclosure in \(<\,>\).
- 5.
It will be convenient to designate a state by enclosure in [ ].
References
Brave Y, Heymann M (1990) Stabilization of discrete-event processes. Int J Control 51:1101–1117
Cassandras CG (1993) Discrete event systems. Irwin
Eilenberg S (1974) Automata, languages, and machines, vol A. Academic Press, Orlando
Germundsson R (1995) Symbolic systems - theory, computation and applications. PhD thesis no. 389, Department of Electrical Engineering, Linköping University
Gunnarsson J (1997) On modeling of discrete event dynamic systems, using symbolic algebraic methods. Thesis no. 502, Division of Automatic Control, Lund University
Heymann M (1990) Concurrency and discrete event control. IEEE Control Syst 10(4):103–112
Hoare, CAR (1985) Communicating sequential processes. Prentice-Hall
Jiao T, Gan Y, Xiao G, Wonham WM (2017) Exploiting symmetry of state tree structures for discrete-event systems with parallel components. Int J Control 90(8):1639–1651
Leduc RJ (2002) Hierarchical interface-based supervisory control. PhD thesis, Department of Electrical and Computer Engineering, University of Toronto
Leduc RJ, Brandin BA, Wonham WM, Lawford M (2001a) Hierarchical interface-based supervisory control: serial case. In: Proceedings of the fortieth IEEE conference on decision and control, Orlando, pp 4116–4121
Leduc RJ, Wonham WM, Lawford M (2001b) Hierarchical interface-based supervisory control: parallel case. In: Proceedings of the thirty-ninth annual Allerton conference on communications, control, and computing, Allerton, pp 386–395
Leduc RJ, Lawford M, Wonham WM (2001c) Hierarchical interface-based supervisory control: AIP example. In: Proceedings of the thirty-ninth annual Allerton conference on communications, control, and computing, Allerton, pp 396–405
Leduc RJ, Brandin BA, Lawford M, Wonham WM (2005a) Hierarchical interface-based supervisory control, part I: serial case. IEEE Trans Autom Control 50(9):1322–1335
Leduc RJ, Lawford M, Wonham WM (2005b) Hierarchical interface-based supervisory control, part II: parallel case. IEEE Trans Autom Control 50(9):1336–1348
Ma C (2004) Nonblocking supervisory control of state tree structures. PhD thesis, Department of Electrical and Computer Engineering. University of Toronto
Ma C, Wonham WM (2003) Control of state tree structures. In: Proceedings of the eleventh IEEE Mediterranean conference on control and automation, Rhodes, Greece, paper T4–005 (6 pp)
Ma C, Wonham WM (2005a) A symbolic approach to the supervision of state tree structures. In: Proceedings thirteenth IEEE Mediterranean conference on control and automation (MED ’05). Limassol, Cyprus, pp 908–913
Ma C, Wonham WM (2005b) Nonblocking supervisory control of state tree structures. Lecture notes in control and information sciences (LNCIS), vol 317. Springer
Milner R (1989) Communication and concurrency. Prentice-Hall
Nooruldeen A, Schmidt KW (2015) State attraction under language specification for the reconfiguration of discrete event systems. IEEE Trans Autom Control 60(6):1630–1634
Ramadge PJ (1983) Control and supervision of discrete event processes. PhD thesis, Department of Electrical Engineering, University of Toronto
Ramadge PJ, Wonham WM (1981) Algebraic decomposition of controlled sequential machines. In: Eighth Triennial World Congress, International Federation Automatic Control (IFAC), Kyoto. Preprints, vol 3, pp 37–41
Ramadge PJ, Wonham WM (1982a) Supervision of discrete event processes. In: Proceedings of the twenty-first IEEE conference on decision and control, New York, pp 1228–1229
Ramadge PJ, Wonham WM (1982b) Supervisory control of discrete event processes. Joint workshop on feedback and synthesis of linear and nonlinear systems, Istituto di Automatica, University di Roma. In: Hinrichsen D, Isidori A (eds) Feedback control of linear and nonlinear systems. Lecture notes on control and information sciences, vol 39. Springer, Berlin, pp 202–214
Ramadge PJ, Wonham WM (1984) Supervisory control of a class of discrete event processes. In: Bensoussan A, Lions JL (eds) Proceedings of the sixth international conference on analysis and optimization of systems, Nice, June 1984. Analysis and optimization of systems, Lecture notes on control and information sciences, Part 2, vol 63. Springer, Berlin, pp 477–498
Ramadge PJ, Wonham WM (1987) Supervisory control of a class of discrete event processes. SIAM J Control Optim 25(1):206–230
Su R (2004) Distributed diagnosis for discrete-event systems. PhD thesis, Department of Electrical and Computer Engineering, University of Toronto
Su R, Wonham WM (2001) Supervisor reduction for discrete-event systems. In: Conference on information sciences and systems, The Johns Hopkins University, 21–23 March 2001, [6 pp]
Su R, Wonham WM (2004) Supervisor reduction for discrete-event systems. Discret Event Dyn Syst 14(1):31–53
Theunissen RJM, Petreczky M, Schiffelers RRH, van Beek DA, Rooda JE (2010) Application of supervisory control synthesis to MRI scanners: improving evolvability. SE Report: Nr. 2010-06, Eindhoven, Apr 2010
Vaz A, Wonham WM (1985) On supervisor reduction in discrete event systems. In: Proceedings of the twenty-third annual Allerton conference on communication, control and computing, University of Illinois, Urbana, pp 933–939
Vaz AF, Wonham WM (1986) On supervisor reduction in discrete-event systems. Int J Control 44(2):475–491
Viswanadham N, Narahari Y (1992) Performance modeling of automated manufacturing systems. Prentice-Hall
Wong KC (1998) On the complexity of projections of discrete-event systems. In: Proceedings of the international workshop on discrete event systems (WODES ’98). Cagliari, pp 201–206
Wonham WM, Ramadge PJ (1984) On the supremal controllable sublanguage of a given language. In: Proceedings of the twenty-third IEEE conference on decision and control, New York, pp 1073–1080
Wonham WM, Ramadge PJ (1987) On the supremal controllable sublanguage of a given language. SIAM J Control Optim 25(3):637–659
Zhang ZH (2001) Smart TCT: an efficient algorithm for supervisory control design. MASc thesis, Department of Electrical and Computer Engineering, University of Toronto
Zhang ZH, Wonham WM (2001) STCT: an efficient algorithm for supervisory control design. In: Caillaud B, Xie X (eds) Proceedings of the symposium on the supervisory control of discrete event systems (SCODES ’01), INRIA, Paris, pp 82–93. See also: Caillaud B et al (eds) (2002) Synthesis and control of discrete event systems, Kluwer, pp 77–100
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Appendix 3.1
Appendix 3.1
EVENT CODING FOR SMALL FACTORY
FACTSUP # states: 12 state set: 0...11 initial state: 0
marker states: 0
# transitions: 24
transition table:
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:
FACTSUP printed.
SIMFTSUP # states: 3 state set: 0...2 initial state: 0
marker states: 0
# transitions: 16
transition table:
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:
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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