Optimal control of discrete event systems: I
Supervisory control for discrete event systems (DESs) belongs essentially to the logic level for control problems in DESs. In this chapter, we study a new optimal control problem in DESs. The performance measure is to maximize the maximal discounted total reward among all possible strings (i.e., paths) of the controlled system. The condition we need for this is only that the performance measure is well defined. By using the method and ideas presented in Chapter 2 for MDPs, we divide the problem into three subcases where the optimal values are, respectively, finite, positive infinite, and negative infinite. We then show the validity of the optimality equation in the case with a finite optimal value. Also, we characterize the optimality equation together with its solutions and characterize the structure of the set of all optimal policies. Based on the above results, we give a link between this performance model with the supervisory control for DESs. Finally, we apply these equations and solutions to a resource allocation system.
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