R-step Relative Copredictability of Decentralized Failure Prognosis in Discrete-Event Systems

Abstract

Recently, failure prediction of discrete-event systems (DESs) has received increasing attention. In this paper, the problem of relative predictability of decentralized failure prognosis in DESs is investigated. The notion of r-step relative copredictability is formalized under the decentralized framework to capture the feature that the occurrence of at least a failure event can be predicted prior to steps at most based on at least one local observation. It is deducted that the relative copredictability is weaker than copredictability and relative predictability. In order to achieve the prediction performance of a decentralized system, the necessary and sufficient condition for verifying the relative copredictability is presented. And a polynomial-complexity algorithm is developed to test the relative copredictability and compute the boundary number of steps prior to the occurrences of failure events. Furthermore, some examples are provided to illustrate the presented results. It is worth noting that the reported work generalizes the main results of relative predictability from the centralized systems to the decentralized setting and extends the results of copredictability introduced by Fuchun Liu to general cases.