Reliable Co-Prognosability of Decentralized Stochastic Discrete-Event Systems and a Polynomial-Time Verification

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.