On Controllable Languages in Supervisory Control of Discrete Event Systems
The concept of controllable language has been shown to be of prime importance in the theory initiated by Ramadge and Wonham for the supervisory control of discrete event systems. After reviewing the notion of supremal controllable sublanguage L ↑ of a given language L , we introduce and study the new notions of supremal closed and controllable sublanguage L cl ↑ and infimal closed and controllable superlanguage L ↓ of L. We discuss the duality between L ↓ and L ↑ and propose algorithms for the computation of L cl ↑ and L ↓ .
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- E. Chen and S. Lafortune. Dealing with blocking in supervisory control of discrete event systems. In Proc. 28th IEEE Conf. on Decision and Control, 1989.Google Scholar
- S. Eilenberg. Automata, Languages and Machines, Vol. A. Academic Press, New York, 1974.Google Scholar
- J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading, MA, 1979.Google Scholar
- S. Lafortune. On transaction execution in database systems. In C. I. Byrnes, C. F. Martin, and R. E. Saeks, editors, Analysis and Control of Nonlinear Systems, pages 331–336. North-Holland, 1988.Google Scholar
- S. Lafortune and E. Chen. On the infimal closed and controllable superlanguage of a given language. Technical Report No. 1–88, College of Engineering Control Group, University of Michigan, November 1988.Google Scholar
- F. Lin and W. M. Wonham. On the computation of supremal controllable sublanguages. In Proc. 23rd Allerton Conf., September 1985.Google Scholar
- P. J. Ramadge. A note on the fixpoint characterization of supremal controllable sublanguages. In Proc. 1987 Conf. Information Sciences and Systems, Johns Hopkins University, Baltimore, MD, March 1987.Google Scholar
- A. Tarski. A lattice-theoretical fixpoint theorem and its applications. Pacific J. Math., 5:285–309, 1955.Google Scholar
- W. M. Wonham and P. J. Ramadge. Modular supervisory control of discrete-event systems. Math. Control Signals Systems, 1(1):13–1988.Google Scholar