Robust Fault Prognosis of Discrete-Event Systems Against Loss of Observations

Abstract

This article investigates the robust fault prognosis of discrete-event systems (DESs) against the loss of observations of events. To solve this problem, a dilated automaton is generated from the plant by adding an unobservable transition attached to every event subject to loss of observations. We prove the equivalence between the robust prognosability of the plant model and the prognosability of the dilated model. In order to deal with unobservable cycles in the dilated model, a new necessary and sufficient condition of robust prognosability based on diagnoser is presented. Moreover, a polynomial algorithm for the verification of robust prognosability is proposed by constructing the verifier to search the existence of some cycle generated by a faulty trace and an unprognosable trace that run synchronously and keep the identical observation before the fault occurs. Our results generalize previous works on fault prognosis of DESs by taking the loss of observations into account. <i>Note to Practitioners</i>&#x2014;The research in this article is motivated by the problem of fault prognosis in the manufacturing system. If some information used for prediction is lost, can engineers still make correct decisions about the occurrences of fault? This article aims to investigate the approach of assuring the accuracy and reliability of prediction by introducing the notion of robust prognosis. A polynomial-time algorithm of verifying the robust prognosability is proposed by constructing the tester automaton.