On ω-controllability and ω-normality of deds
Ratnesh Kumar, Vijay K. Garg, Steven I. Marcus · 1991
In this paper, 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 [7], [12]. We present the notion of complete languages and show its close relation to ω-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 ω-controllable sublanguage of a given ω-language in terms of the supremal (closed,) complete and controllable sublanguge. The notions of ω-observability and ω-normality are introduced. A necessary and sufficient condition for the existence of a supervisor in case of partial observation is presented in terms of ω-observability. A closed form expression for the supremal ω-normal sublanguage in terms of the supremal closed, complete and normal sublanguage is also presented.