Coordination Control of Discrete-Event Systems Revisited

TL;DR

This paper revisits and extends the coordination control approach for supervisory control of distributed discrete-event systems, addressing non-prefix-closed languages and the complexity of minimal coordinator computation.

Contribution

It simplifies key notions, generalizes to non-prefix-closed languages, and analyzes the NP-hardness of finding minimal coordinators in coordination control.

Findings

Revised and simplified the notions of conditional decomposability, controllability, and closedness.

Extended the framework to non-prefix-closed languages, addressing blocking issues.

Proved NP-hardness of computing minimal coordinators.

Abstract

In this paper, we revise and further investigate the coordination control approach proposed for supervisory control of distributed discrete-event systems with synchronous communication based on the Ramadge-Wonham automata framework. The notions of conditional decomposability, conditional controllability, and conditional closedness ensuring the existence of a solution are carefully revised and simplified. The paper is generalized to non-prefix-closed languages, that is, supremal conditionally controllable sublanguages of not necessary prefix-closed languages are discussed. Non-prefix-closed languages introduce the blocking issue into coordination control, hence a procedure to compute a coordinator for nonblockingness is included. The optimization problem concerning the size of a coordinator is under investigation. We prove that to find the minimal extension of the coordinator event set for which a given specification language is conditionally decomposable is NP-hard. In other words, unless P=NP, it is not possible to find a polynomial algorithm to compute the minimal coordinator with respect to the number of events.