Decentralized fault prognosis of discrete event systems with guaranteed performance bound

We study the problem of decentralized fault prognosis of partially-observed discrete event systems. In order to capture the prognostic performance issue in the prognosis problem, we propose two new criteria: (1) all faults can be predicted K steps ahead; and (2) a fault will occur for sure within M steps once a fault alarm is issued; and we refer to (M,K) as the performance bound of the prognostic system. A necessary and sufficient condition for the existence of a decentralized supervisor satisfying these two criteria is provided, which is termed as (M,K)-coprognosability. A polynomial-time algorithm for the verification of (M,K)-coprognosability is also proposed. Finally, we show that the proposed approach is applicable to both disjunctive and conjunctive architectures. Our results generalize previous work on decentralized fault prognosis.