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 Chapter 1, in Section 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 £(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?
KeywordsControllable Event Regular Language Supervisory Control Unobservable Event Uncontrollable Event
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Book or survey papers on supervisory control
Original references on main concepts presented in this chapter
For further reading on some topics only briefly covered in this chapter
- 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, Vo. 15, No. 2, pp. 111117, August 1990.Google Scholar
Some applications of supervisory control
- Balemi, S., G. J. Hoffmann, P. Gyugyi, H. Wong-Toi, and G. F. Franklin, “Supervisory control of a rapid thermal multiprocessor,” IEEE Transactions on Automatic Control, Vol. 38, No. 7, pp. 1040–1059, July 1993.Google Scholar
- Rudie, K., W.M. Wonham, “Supervisory control of communicating processes,” in Protocol Specification, Testing, and Verification X, L. Logrippo, R. L. Probert, and H. Ural (Eds.), Elsevier Science Publishers, 1990, pp. 243–257.Google Scholar
- Thistle, J.G., R.P. Malhamé, H.-H. Hoang, and S. Lafortune, “Feature interaction modelling, detection and resolution: A supervisory control approach,” in Feature Interactions in Telecommunication Networks IV, P. Dini, R. Boutaba, and L. Logrippo, Eds., IOS Press, 1997, pp. 93–107.Google Scholar