Inference-based Ambiguity Management in Decentralized Decision-Making: Decentralized Control of Discrete Event Systems

Decentralized decision-making requires the interaction of various local decision-makers in order to arrive at a global decision. Limited sensing capabilities at each local site can create ambiguities in a decision-making process at each local site. We argue that such ambiguities are of differing gradations. We propose a framework for decentralized decisionmaking (applied to decentralized control in particular) which allows computation of such ambiguity-gradations, and utilizes their knowledge in arriving at a global decision. Each local decision is tagged with a certain grade or level of ambiguity; zero being the minimum ambiguity level. A global decision is taken to be the same as a "winning" local decision, i.e., one having the minimum level of ambiguity. The computation of an ambiguity level for a local decision requires an assessment of the self-ambiguities as well as the ambiguities of the others, and an inference based up on such knowledge. In order to characterize the class of closed-loop behaviors achievable under the control of such an inference-based decentralized control, we introduce the notion of N-inference-observability, where N is an index representing the maximum ambiguity level of any winning local decision. We show that the C&PVD&Acoobservability is the same as the zero-inference-observability, whereas the conditional C&PVD&A-coobservability is the same as the unity-inference-observability. We also present examples of higher order inference-observable languages.