| In a decentralized control problem where supervisors only possess partial observations of plant event sequences, there may be sequence pairs that are indistinguishable to a supervisor, and that require different control decisions from that supervisor. Injecting communications into the system renders the sequence pairs distinguishable, and thus solves the problem.; A communication state is a place prior to which the communication should occur. When there are cycles in the graph representation of a plant, the task of communication becomes complicated since every sequence pair requires the identification of a communication state, and cycles in the sequence pairs may produce an infinite number of communication states.; It is shown that, contrary to an earlier conjecture in the literature, there are some plants where an arbitrarily large number of different sequence pairs requires that same number of different communication states. This result is established by various counterexamples. It is demonstrated, however, that plants that possess special graphical structures yield cases where infinitely many sequence pairs all share the same communication state. Some of these special structures are identified. |
