Predicates and Predicate Transformers for Supervisory Control of Discrete Event Dynamical Systems

Most discrete event system models are based on defining the alphabet set or the set of events as a fundamental concept. In this paper, we take an alternative view of treating the state space as the fundamental concept. We approach the problem of controlling discrete event systems by using predicates and predicate transformers. Predicates have the advantage that they can concisely characterize an infinite state space. The notion of controllability of a predicate is defined, and the supervisory predicate control problem introduced in this paper is solved. A closed form expression for the weakest controllable predicate is obtained. The problem of controlling discrete event systems under incomplete state observation is also considered and observability of predicates is defined. Techniques for finding extremal solutions of boolean equations is used to derive minimally restrictive supervisors.