Synthesis of Inference-based Decentralized Control for Discrete Event Systems

In our past work (Kumar and Takai, 2005), 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-ambiguities and that 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. In this paper we 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. We show that for the special cases of N = 0 and N = 1, the proposed supervisor achieves the same language as those reported in (Yoo and Lafortune, 2002; Takai et al., 2005) (for N= 0) and (Yoo and Lafortune, 2004) (for N= 1). The synthesized supervisor is parameterized by N (the parameter bounding the ambiguity level), and as N is increased, the supervisor becomes more permissive