Decentralized supervisory control with coalgebra

Coalgebraic methods provide new results and insights for the supervisory control of discrete-event systems (DES). In this paper a coalgebraic framework for the decentralized control of DES is proposed. The paper is based on the formalism developed for the supervisory control of DES in the partial observation case, the notion of bisimulation, and its generalizations (partial bisimulation, co-observability and control relation). Local indistinguisha-bility relations are used in the relational characterizations of co-observability. Conjunctive and permissive (C&P) as well as disjunctive and antipermissive (D&A) versions of co-observability are captured by their corresponding relations. Coinduction is used to define a new operation on languages called C&P supervised product. Existence of a supervisor that achieves a given specification in the closed-loop system is equivalent to the existence of a partial bisimulation relation, which is at the same time a co-observability and control relation.