Synthesis of Inference-Based Decentralized Control for Discrete Event Systems

In our past work, we presented a framework for the decentralized control of discrete event systems involving inferencing over ambiguities, about the system state, of various local decision makers. Using the knowledge of the self-ambiguity and those of the others, each local control decision is tagged with a certain ambiguity level (level zero being the minimum and representing no ambiguity). A global control decision is taken to be a “winning'' local control decision, i.e., one with a minimum ambiguity level. For the existence of a decentralized supervisor, so that for each controllable event the ambiguity levels of all winning disablement or enablement decisions are bounded by some number $N$ (such a supervisor is termed $N$-inferring), the notion of $N$-inference-observability was introduced. When the given specification fails to satisfy the $N$-inference-observability property, an $N$-inferring supervisor achieving the entire specification does not exist. We first show that the class of $N$-inference-observable sublanguages is not closed under union implying that the supremal $N$-inference-observable sublanguage need not exist. We next provide a technique for synthesizing an $N$-inferring decentralized supervisor that achieves an $N$-inference-observable sublanguage of the specification. The sublanguage achieved equals the specification language when the specification itself is $N$-inference-observable. A