Formal modeling and synthesis of state-transferring communication among decentralized supervisors for discrete-event systems

This work proposes to model and synthesize communicating decentralized supervisors for a discrete-event system (DES) within the framework of distributed supervised discrete-event systems (DSDESs), which was introduced by the authors. To this end, first a polynomial dynamical system (PDS) representation for DSDESs is derived, which reveals the informational dependencies of distributed supervisors. To serve these dependencies, communication between every two supervisors is modeled by a communication event, whose semantics is defined by a map from observable events of the issuer of the communication to its variables, employed by the PDS representation. Thereby, the synthesis of communicating decentralized supervisors is reduced to the design of these maps using standard algebraic tools. The approach is illustrated through formal design of an information policy.