Optimal control of discrete event systems: II

In this chapter, we present another model for optimal control of DESs with an arbitrary control pattern. This model differs from that in Chapter 7 in three ways. First, the discrete event system is defined as a collection of event sets that depend on strings. Whenthe system generates a string, the next event that occurs should be in the corresponding event set. Second, the rewards are for choosing control inputs at strings. Finally, the control pattern (which consists of sets of available control inputs) depends on strings. The performance measure is to find a supervisor under the condition where the discounted total reward among strings from the initial state is maximized. Similarly to Chapter 7, we study the problem also by applying ideas from Chapter 2 for Markov decision processes. Surely, the problem here is more complex than that in Chapter 7. Moreover, we present a new supervisory control problem of DESs with the control pattern being dependent on strings. We study the problem in both event feedback control and state feedback control by generalizing concepts of invariant and closed languages/predicates from the supervisory control literature. Finally, we apply our model and the results to a job-matching problem.