Supervisory control with partial information on controllability and observability

In supervisory control it is assumed that the set of events is partitioned in terms of controllability and observability into subsets of controllable and uncontrollable events, and observable and unobservable events. It is assumed that these partitions are properties of the system, are given from the start and, are unchanging throughout the life of the process. In this paper we extend the existing framework of supervisory control of discrete event systems to incorporate uncertainty due to the presence of events whose controllability or observability is unknown. There are situations, however, in which it is not known apriori whether an event is controllable or not. Similarly, the observability status of certain events may be unknown. We are thus lead to consideration of a finer partition of the event set into three subsets of controllable events, uncontrollable events and a subset of events whose controllability status is unknown (similarly for observability). Conditions for the solvability of this problem are obtained.