Supervisory Control of Distributed Systems: Conflict Resolution

Abstract

In distributed synthesis and control, one well-known potential hazard is conflict between modular designs. In a modular approach to the supervisory control of discrete-event systems, modular supervisors that are individually nonblocking (with respect to the plant) may nevertheless conflict and thus produce blocking, or even deadlock, when operating concurrently. A scheme of resolving this potential conflict between the modular supervisors would be to accord priorities to the conflicting supervisors. When conflict arises, the modular supervisor that is assigned a higher priority will have sole control, or in other words the control action of the lower priority supervisor will be suspended. Thus by assigning priority appropriately, control actions of the modular supervisors will be suspended and reactivated in such a way that the potential conflict can be averted. In this article we formalize this scheme with reporter maps from a hierarchical approach to the supervisory control of discrete-event systems. These maps, each acting as an interface between a modular supervisor and the plant, mediate the flow of information and control, and thus in this way achieve suspension and reactivation of the modular supervisors. Sufficient conditions on these reporter maps for conflict resolution are obtained. Roughly speaking, the conditions are that (1) the reporter maps select suitable ‘subsystems’ of the plant; (2) within these subsystems, conflicts are ‘resolved’; (3) the reporter maps are ‘refined’ enough to lift these local conflict resolutions back to the original plant. With these conditions, a constructive solution is developed, which in essence suspends a supervisor ‘just in time’ to prevent conflict and reactivates it when the plant and the other supervisor return to the state they were in when the suspension began. Examples inspired by the feature interaction problem in telecommunication systems are provided for illustration.