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Abstract

The situation under consideration in this chapter is that of a given DES, modeled at the untimed (or logical) level of abstraction, and whose behavior must be modified by feedback control in order to achieve a given set of specifications. This is reminiscent of the feedback control loop introduced in  Chap. 1, in Sect. 1.2.8. Let us assume that the given DES is modeled by automaton G, where the state space of G need not be finite. Let E be the event set of G. Automaton G models the “uncontrolled behavior” of the DES. The premise is that this behavior is not satisfactory and must be “modified” by control; modifying the behavior is to be understood as restricting the behavior to a subset of L(G). In order to alter the behavior of G we introduce a supervisor; supervisors will be denoted by S. Note that we separate the “plant” G from the “controller” (or supervisor) S, as is customary in control theory. This raises two questions: (a) What do we mean by specifications? and (b) How does S modify the behavior of G?

Keywords

Controllable Event Fusion Rule Regular Language Supervisory Control Unobservable Event 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Selected References

∎ Book or survey papers on supervisory control

  1. —Kumar, R., and V.K. Garg, Modeling and Control of Logical Discrete Event Systems, Kluwer Academic Publishers, Boston, 1995.MATHGoogle Scholar
  2. — Ramadge, P.J., and W.M. Wonham, “The control of discrete event systems,” Proceedings of the IEEE, Vol. 77, No. 1, pp. 81–98, 1989.CrossRefGoogle Scholar
  3. — Thistle, J.G., “Supervisory control of discrete event systems,” Mathematical and Computer Modelling, Vol. 23, No. 11/12, pp. 25–53, 1996.MATHCrossRefMathSciNetGoogle Scholar

∎ Selected original references on main results presented in this chapter

  1. — Brandt, R.D., V. Garg, R. Kumar, F. Lin, S.I. Marcus, and W.M. Wonham, “Formulas for calculating supremal controllable and normal sublanguages,” Systems & Control Letters, Vol. 15, No. 2, pp. 111–117, 1990.MATHCrossRefMathSciNetGoogle Scholar
  2. — Chen, E., and S. Lafortune. “Dealing with blocking in supervisory control of discrete event systems,” IEEE Transactions on Automatic Control, Vol. 36, No. 6, pp. 724–735, 1991.CrossRefMathSciNetGoogle Scholar
  3. — Cieslak, R., C. Desclaux, A. Fawaz, and P. Varaiya, “Supervisory control of discrete-event processes with partial observations,” IEEE Transactions on Automatic Control, Vol. 33, No. 3, pp. 249–260, 1988.MATHCrossRefGoogle Scholar
  4. — Lafortune, S., and E. Chen, “The infimal closed controllable superlanguage and its application in supervisory control,” IEEE Transactions on Automatic Control, Vol. 35, No. 4, pp. 398–405, 1990.MATHCrossRefMathSciNetGoogle Scholar
  5. — Lamouchi, H., and J.G. Thistle, “Effective control synthesis for DES under partial observations,” Proceedings of the 39th IEEE Conference on Decision and Control, pp. 22–28, 2000.Google Scholar
  6. — Lin, F., and W.M. Wonham, “On observability of discrete-event systems,” Information Sciences, Vol. 44, pp. 173–198, 1988.MATHCrossRefMathSciNetGoogle Scholar
  7. — Ramadge, P.J., and W.M. Wonham, “Supervisory control of a class of discrete event processes,” SI AM Journal on Control and Optimization, Vol. 25, No. 1, pp. 206–230, 1987.MATHCrossRefMathSciNetGoogle Scholar
  8. — Rudie, K., and W.M. Wonham, “Think globally, act locally: Decentralized supervisory control,” IEEE Transactions on Automatic Control, Vol. 37, No. 11, pp. 1692–1708, 1992.MATHCrossRefMathSciNetGoogle Scholar
  9. — Rudie, K., and W.M. Wonham, “The infimal prefix-closed and observable super-language of a given language,” Systems & Control Letters, Vol. 15, pp. 361–371, 1990.MATHCrossRefMathSciNetGoogle Scholar
  10. — Tsitsiklis, J.N., “On the control of discrete-event dynamical systems,” Mathematics of Control, Signals, and Systems, Vol. 2, No. 1, pp. 95–107, 1989.MATHCrossRefMathSciNetGoogle Scholar
  11. — Wonham, W.M., and P.J. Ramadge, “On the supremal controllable sublanguage of a given language,” SIAM Journal on Control and Optimization, Vol. 25, No. 3, pp. 637–659, 1987.CrossRefMathSciNetGoogle Scholar
  12. — Wonham, W.M., and P.J. Ramadge, “Modular supervisory control of discrete-event systems,” Mathematics of Control, Signals, and Systems, Vol. 1, No. 1, pp. 13–30, 1988.MATHCrossRefMathSciNetGoogle Scholar
  13. — Yoo, T.-S., and S. Lafortune, “A general architecture for decentralized supervisory control of discrete-event systems,” Discrete Event Dynamic Systems: Theory – Applications, Vol. 12, No. 3, pp. 335–377, 2002.MATHCrossRefMathSciNetGoogle Scholar

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© Springer Science+Business Media, LLC 2008

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