Inference-based ambiguity management in decentralized decision-making: decentralized diagnosis of discrete event systems

The task of decentralized decision-making involves interaction of a set of local decision-makers, each of which operates under limited sensing capabilities and is thus subjected to ambiguity during the process of decision-making. In a prior work by R. Kumar and S. Takai (2005) we made a key observation that such ambiguities are of differing gradations and presented a framework for inferencing over various local control decisions of varying ambiguity levels to arrive at a global control decision. We develop a similar framework for performing diagnosis in a decentralized setting. For each event-trace executed by a system being monitored, each local diagnoser issues its own diagnosis decision (failure or non-failure or unsure), tagged with a certain ambiguity level zero being the minimum). A global diagnosis decision is taken to be a "winning" local diagnosis decision, i.e., one with a minimum ambiguity level. 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 systems for which any fault can be detected within a uniformly bounded delay, we introduce the notion of N-inference-diagnosability for failures (also called N-inference-diagnosability), where the index N represents the maximum ambiguity level of any winning local decision. We show that the codiagnosability introduced by W. Qiu and R. Kumar (2006) is the same as 0-inference F-diagnosability; the conditional F-codiagnosability introduced by Y. Wang et al.(2004), Y. Wang et al. (2005) is a type of 1-inference F-diagnosability; and the class of higher-index inference F-diagnosable systems strictly subsumes the class of lower-index ones