Rui Zhao

Fault prognosis of discrete-event systems (DESs) aims to predict the occurrence of fault beforehand such that certain protective measures may be adopted before the fault occurs. This article investigates the reliable coprognosability issue for decentralized stochastic DESs (SDESs) facing the possible unavailability of some local agents. The main contributions are as follows. First, we formalize the notion of $r$ -reliable coprognosability for SDESs. In general, an $r$ -reliably coprognosable SDES with $n$ local sites $(1 \leq r \leq n)$ can predict the occurrences of faults even though $n-r$ local agents are invalid. Second, we construct a reliable coprognoser from the given stochastic system and present a necessary and sufficient condition for testing $r$ -reliable coprognosability by the reliable coprognoser. Third, due to the exponential complexity of testing $r$ -reliable coprognosability by reliable coprognoser, a reliable coverifier is constructed and an alternate necessary and sufficient condition for verifying $r$ -reliable coprognosability of SDESs by the reliable coverifier is proposed, which is polynomial time.

Safe diagnosability of discrete-event systems (DESs) is viewed as the first necessary step of fault-tolerant supervision in the literature. For safe diagnosable systems, it is required that not only failures occurring in systems can be detected within a finite delay, but also the detection should be completed before running any unsafe operation. In this paper, we present a novel approach to deal with the safe diagnosis issue for stochastic DESs by constructing a nondeterministic automaton called the safe verifier, and the necessary and sufficient condition for safe diagnosability of stochastic DESs is presented. It is worth noting that the proposed approach has lower complexity than the existing approach based on safe diagnoser as far as the number of states.

In this paper, the problem of relative predictability of failure event occurrences is investigated. The notion of relative predictability is proposed for logical automata and the concept of predictable rate is introduced to characterise the predictability property of a discrete-event system, which takes values in the interval [0, 1]. Intuitively, a discrete-event system being relatively predictable means that there exist some failure events which can be predicted from the observations of the system. The relationship between relative predictability and predictability introduced by Sahika Genc et al. analysed and the analysis shows that relative predictability is weaker than predictability for discrete-event systems. Furthermore, a necessary and sufficient condition for relative predictability is presented. In particular, an opacity-based algorithm is developed to test the relative predictability, which is polynomial in the number of states of the system. Also, some examples are provided to illustrate the presented results.