A computer implementable algorithm for the synthesis of an optimal controller for acyclic discrete event processes

An optimal control theory for designing a controller, that selects unique control actions is developed for controlling discrete event systems (DESs). Prior work on supervisor synthesis problems studied the design of supervisors for satisfying qualitative specifications within the framework of the DESs. In this paper we define and investigate the synthesis of an optimal controller in the sense that, regardless the state of the plant, the worst cost of all surviving paths from that state to the set of frontier marked states is minimized. Our work differs from prior works on optimal control of DESs in that the controller selects a unique controllable event to be executed per state, rather than a set of admissible controllable events. An efficient algorithm is provided to solve this problem under complete observation.