Semi-Tensor Product of Matrices Approach to the Problem of Fault Detection for Discrete Event Systems (DESs)

This brief focuses on presenting a state-based matrix approach to the problem of fault detection for discrete event systems (DESs). Firstly, the given system is modeled as a finite state machine and converted into algebraic structure with the help of semi-tensor product of matrices. Assuming that the faults influence only the state transition and can't recover, there are two possible constructions for the system: a normative and a faulty one. Considering the evolutionary process for the two systems, labeled correlative matrices between current state and initial state are established, respectively, which have an advantage in computer storage compared with existent methods. And then, a theorem is proposed as a criterion of detectable faults, followed with a corresponding algorithm to verify whether the faults are detectable for a given system. Finally, the approach in this brief is tested effectively for the exhaust gas recirculation system.