(A) study on optimal supervisory control for discrete event systems

Abstract

A discrete event system (DES) is a dynamic system whose state transitions are caused by physical phenomena, called events, occurring abruptly at unknown irregular intervals. Examples include manufacturing systems, computer and communication networks and traffic systems. The supervisory control theory (SCT) is recognized as one of effective tools for the analysis and control of the DESs. In SCT, the control objective is to restrict the plant behavior such that(s.t.) it remains confined within a specific range. Recently, there has also been many studies considering the optimal supervisory control problem (OSCP) in which the control objective is to restrict the system behavior so that a certain cost function defined along the trajectory of the system is optimized. In the OSCP, it is impossible to optimize the system for all aspects. For example, in order to complete a task in short time, we have to consume a lot of energy. Thus, we have to decide what we optimize and then define the cost function which is suitable to our purpose. In this dissertation, we study optimal control problems for the DESs. First, we formulate the OSCP with the cost function using the disabling costs of the events and the penalties of the states which is useful in the system design. Then, we devise an algorithm to design the optimal nonblocking supervisor to solve the problem. Since the proposed algorithm has polynomial-order computational complexity, we can solve the problem efficiently. Then, we formulate the power distribution network restoration problem to an OSCP and solve it using the proposed algorithm as a case study. Next, we extend the results to the partial observation cases. In the OSCP under partial observation, the optimal supervisor for the given DES has restrictions that it must makes the controlled system``s behavior observable as well as it is a nonblocking supervisor. Although the proposed algorithm to design optimal nonblocking supervisor (ONS) under partial observation...