Robust predictability of stochastic discrete-event systems and a polynomial-time verification

The purpose of fault prediction of discrete-event systems (DESs) is to predict the occurrence of fault in advance such that some protective actions can be taken before the occurrence of the fault. The robust predictability issue under the framework of stochastic DESs (SDESs) with model uncertainty is studied. First, the notions of (ϵ,m)−robust predictability and robust predictability of SDESs are formalized. In general, a set of stochastic systems being robustly predictable can predict the occurrences of faults in the sense of probability. Then the robust predictor and robust verifier for performing the robust prediction are constructed from the given possible stochastic systems. Particularly, the necessary and sufficient conditions for (ϵ,m)−robust predictability and robust predictability of SDESs are proposed, and an approach is presented to verify the robust predictability of SDESs with polynomial-time complexity both in the state space and in the number of all possible models.