Supervisor Localization: A Top-Down Approach to Distributed Control of Discrete-Event Systems

Abstract

We study distributed control design for discrete-event systems (DES) in the framework of supervisory control theory. Our DES comprise multiple agents, acting independently except for specifications on 'global' behavior. The central problem investigated is how to synthesize 'local' controllers for individual agents such that the resultant controlled behavior is identical with that achieved by global supervision.The investigation is carried out with both language-and state-based models. In the language-based setting, a supervisor localization algorithm is developed that solves the problem in a top-down fashion: first, compute a global supervisor, then decompose it into local controllers. For large-scale DES where a global supervisor might not be feasibly computable owing to state explosion, a decomposition-aggregation solution procedure is established. In the state-based setting, specifically that of 'state tree structures' (STS), a counterpart supervisor localization algorithm is developed having potential to exploit the known efficiency of STS for large-DES control design.ii Acknowledgements It is my great honour and pleasure to study under the supervision of Professor W.M.Wonham, to whom I would like to express my deepest gratitude for his patient guidance and inspiring comments throughout the course of study. Learning closely from him, I have begun to understand and appreciate the rigorous attitude and systematic methodology toward research, the far-reaching value being unmeasurable in terms of the amount of knowledge. In addition, I am grateful to him and his wife, Anne, for their warm care and help in life.

Supervision localization of timed discrete-event systems

“…Continuing the example in Fig. 1, let plant G be composed of three agents G k with event sets Σ k , k ∈ [1,3]. Suppose σ1, σ2 ∈ Σ1, σ2, σ3 ∈ Σ2, and σ3, σ4, σ5 ∈ Σ3; thus G1 and G2 share event σ2, and G2 and G3 share event σ3.…”

“…Compared to [3], the present supervisor localization is an extension from untimed DES to TDES. As will be seen below, the treatment of prohibitible events is the timed counterpart of the treatment of controllable events in [3]; on the other hand, localization of forcible events' preemptive action is specific to TDES, and we introduce below the new concept "local preemptor". Further, we will discuss applying supervisor localization to the distributed control of multi-agent TDES.…”

“…Then in terms of language, the above condition means that for all s ∈ Σ * and σ ∈ Σ, there holds (cf. [3])…”

“…The principal contribution of this paper is the development of a timed supervisor localization theory in the BW TDES framework, which extends the untimed counterpart in [3,4]. In this timed localization, a novel feature is "event forcing" as means of control, in addition to the usual "event disabling".…”

“…Recently we developed a top-down approach, called supervisor localization [3,4] to the distributed control of untimed discrete-event systems (DES) in the RamadgeWonham (RW) supervisory control framework [10,14]. We view the plant to be controlled as comprised of independent asynchronous agents which are coupled implicitly through logical control specifications.…”