Model Properties for Efficient Synthesis of Nonblocking Modular Supervisors

Supervisory control theory provides means to synthesize supervisors for cyber-physical systems from models of the uncontrolled plant and models of the control requirements. It has been shown that in general supervisory control synthesis is NP-hard. However, for several industrial systems supervisory control synthesis verifies that the provided control requirements are sufficient to act as a supervisor. In this paper, we propose model properties and a method to identify when no synthesis is needed for a given set of plant models and requirement models, i.e., the plant models and requirement models together form a maximally permissive, controllable, and nonblocking supervisor. The method consists of creating a control problem dependency graph and verifying whether it is acyclic to establish that synthesis can be skipped. In case of a cyclic graph, potential blocking issues can be localized, so that the original control problem can be reduced to only synthesizing supervisors for smaller partial control problems. The proposed method is illustrated in detail with a case study of a production line and applied on a case study of a roadway tunnel for which the method identifies a large part of the system that requires no synthesis.