Robust Fault Diagnosis of Stochastic Discrete Event Systems

Abstract

We investigate the problem of robust fault diagnosis of stochastic discrete-event systems against model uncertainty. In this problem, we assume that the actual behavior of the system is unknown a priori and the true model of the system belongs to a set of possible models described by probabilistic automata. The goal of this problem is to almost successfully detect the occurrence of fault in the sense that, first, no false alarm can be made, and second, the misdetection rate is smaller than a given threshold $\epsilon$ after some delay $K$ even without knowing the true model a priori . A condition termed as robust $(\epsilon,K)$ -diagnosability is proposed to capture the existence of such a robust diagnoser that satisfies the above-mentioned requirements. We also propose the notions of robust $\epsilon$ -diagnosability and robust A-diagnosability, which require that a given misdetection rate $\epsilon$ can be achieved with some delay and any arbitrarily small misdetection rate can be achieved, respectively. For each condition, an effective verification algorithm is also proposed. Our results generalize previous works on fault diagnosis of stochastic discrete-event systems by taking model uncertainty and specific misdetection rate into account.