Abstract
This paper deals with the efficient on-line calculation of supervisory controls for discrete event systems (DES's) in the framework of limited lookahead control policies (or LLPs) that we introduced in previous papers. In the LLP scheme, the control action after a given trace of events has been executed is calculated on-line on the basis of anN-step ahead projection of the behavior of the DES. To compute these controls, one must calculate after the execution of each event the supremal controllable sublanguage of a finite language with respect to another finite larger language. In our previous work, we showed how the required supremal controllable sublanguage calculation can be performed by using a backward dynamic programming algorithm over the nodes of the tree representation of these two languages. In this paper, we pursue the same approach for the calculation of LLP controls, but instead we adopt a forward calculation procedure over theN-level tree of interest. This forward procedure improves upon previous work by avoiding the explicit consideration of all the nodes of theN-level tree, while still permitting tree-to-tree recursiveness as enabled events are executed by the system. The forward search ends whenever a control decision can be made unambiguously or whenever the boundary of theN-level tree is reached, whichever comes first. This motivates the name “Variable Lookahead Policy” (or VLP) for this implementation of the LLP supervisory control scheme. This paper presents a general VLP algorithm and studies the properties of several special cases of it. The paper also discusses the implementation of the VLP algorithms and presents computational results regarding the application of these algorithms to a “time-varying” DES.
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S. L. Chung, S. Lafortune, and F. Lin. Limited lookahead policies in supervisory control of discrete event systems.IEEE Trans. Automatic Control, 37(12):1921–1935, December 1992.
S. L. Chung, S. Lafortune, and F. Lin. Recursive computation of limited lookahead supervisory controls for discrete event systems.Journal of Discrete Event Dynamic Systems: Theory and Applications, 3(1):71–100, March 1993.
S. L. Chung, S. Lafortune, and F. Lin. Supervisory control using variable lookahead policies. InProc. 1993 American Control Conf., pp. 1203–1208, San Francisco, CA, June 1993.
S. L. Chung, S. Lafortune, and F. Lin. Supervisory control with variable lookahead policies: Illustrative example. In S. Balemi, P. Kozák, and R. Smedinga, editors,Discrete Event Systems: Modeling and Control-Proceedings of a Joint Workshop on Discrete Event Systems, pp. 207–214. Birkhäuser Basel Verlag, 1993.
C. A. R. Hoare.Communicating Sequential Processes. International Series in Computer Science. Prentice-Hall, Englewood Cliffs, NJ, 1985.
K. M. Inan and P. P. Varaiya. Algebras of discrete event models.Proc. IEEE. 77(1):24–38, January 1989.
F. Lin and W. M. Wonham. On observability of discrete-event systems.Information Sciences, 44:173–198, 1988.
T. Murata. Petri nets: Properties, analysis, and applications.Proc. IEEE, 77(4):541–580, April 1989.
J. L. Peterson,Petri Net Theory and The Modelling of Systems. Prentice-Hall, 1981.
P. J. Ramadge and W. M. Wonham. Supervisory control of a class of discrete event processes.SIAM J. Control and Optimization, 25(1):206–230, January 1987.
P. J. Ramadge and W. M. Wonham. The control of discrete event systems.Proc. IEEE 77(1):81–98, January 1989.
W. M. Wonham and P. J. Ramadge. On the supremal controllable sublanguage of a given language.SIAM J. Control and Optimization, 25(3):637–659, May 1987.
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Chung, SL., Lafortune, S. & Lin, F. Supervisory control using variable lookahead policies. Discrete Event Dyn Syst 4, 237–268 (1994). https://doi.org/10.1007/BF01438709
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DOI: https://doi.org/10.1007/BF01438709