Synthesizing deterministic controllers in supervisory control

Supervisory control theory for discrete event systems is based on finite state automata whose inputs are partitioned into controllable and uncontrollable events. Well-known algorithms used in the Ramadge-Wonham framework disable or enable controllable events such that it is finally possible to reach designated final states from every reachable state. However, as these algorithms compute the least restriction on controllable events, their result is usually a nondeterministic automaton that can not be directly implemented. For this reason, one distinguishes between supervisors (directly generated by supervisory control) and controllers that are further restrictions of supervisors to achieve determinism. Unfortunately, controllers that are generated from a supervisor may be blocking, even if the underlying discrete event system is nonblocking. In this paper, we give a modification of a supervisor synthesis algorithm that enables us to derive deterministic controllers. Moreover, we show that the algorithm is both correct and complete, i.e., that it generates a deterministic controller whenever one exists.