| For a given discrete-event plant G, to find decentralized supervisors that under their control the system behaves exactly like the legal behavior E, there are two conditions: controllability and coobservability. When E is controllable and observable but not coobservable, communications of event occurrences between supervisors will be needed. A new property called transition-based coobservability is defined and it is proven that transition-based coobservability together with controllability are necessary and sufficient conditions for solving the decentralized problem. To check transition-based coobservability, an automaton, called a modified M-machine, is constructed. It is proven that the system is not transition-based coobservable if and only if there is a path from the initial state to the marked state in this automaton. An algorithm is also given to compute a communication protocol between supervisors so that the system is transition-based coobservable and the communications are consistent. |
