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?
KeywordsControllable Event Fusion Rule Regular Language Supervisory Control Unobservable Event
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- — 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