ON SUPERVISORY CONTROL OF SEQUENTIAL BEHAVIORS

We address the supervisory synthesis problem for controlling the sequential behaviors of discrete event dynamical systems (DEDS's) under complete, as well as partial information through the use of synchronous composition of the plants and the supervisors. We present the notion of complete languages, discuss some of its algebraic properties, and show its close relation to omega-languages. We prove that the supremal (closed) complete and controllable sublanguage of a given language exists, and present an algorithm to compute it. We present a closed-form expression for the supremal omega-controllable sublanguage of a given omega-language in terms of the supremal (closed) complete and controllable sublanguage. This closed-form expression suggests that certain operations on a given omega-language can alternatively be achieved by performing certain other similar operations on its prefix (which is a finite language) and then taking the limit (to obtain the desired omega-language). A necessary and sufficient condition for the existence of a supervisor in case of partial observation is presented in terms of omega-observability. Notion of omega-normality is also introduced, and a closed-form expression for the supremal omega-normal sublanguage, in terms of the supremal closed, complete, and normal sublanguage, is presented.