On tolerable and desirable behaviors in supervisory control of discrete event systems

In general terms, the supervisory control problem for discrete event systems consists of designing a controller such that the controlled system satisfies a given set of requirements that involve event ordering. In the problem formulation considered, the requirements for the behavior (i.e., set of traces) of the controlled system are specified in terms of a desired behavior and a larger tolerated behavior. Due to uncontrollable events, behavior outside of the ideal desired behavior may be tolerated if overall this results in achieving more of the desired behavior. The solution of this problem in both the general case and the nonblocking case is studied. While the general solution can be completely characterized using operations currently known in supervisory control theory, the nonblocking solution requires the study of another class of controllable languages. A discussion of this class is given