ON CONTROLLABILITY AND NORMALITY OF DISCRETE EVENT DYNAMIC-SYSTEMS

This paper studies the supervisor synthesis problem of Discrete Event Dynamical Systems (DEDS's) through the use of synchronous composition of the plant and the supervisor and discusses some of the simplifications achieved by using the synchronous composition to model supervisory control. An alternate definition of controllability is presented. This definition of controllability is then used to derive an algorithm that is computationally more efficient than previously existing ones for the construction of the supremal controllable sublanguage; the algorithm is also shown to be optimal. The observability and normality issues arising due to the partial observation of the system dynamics under an arbitrary mask are then investigated. Closed form representations of the supremal normal, and supremal closed and normal sublanguages are derived in the more general setting of arbitrary mask and nonclosed languages, thus extending earlier results of the authors and others.