Synthesis of Inference-Based Decentralized Control for Discrete Event Systems
Shigemasa Takai, Ratnesh Kumar · IEEE Transactions on Automatic Control · 2008
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-observablesublanguageof the specification. The sublanguage achieved equals the specification language when the specification itself is$N$-inference-observable. A