State-Based Decentralized Diagnosis of Bi-Fuzzy Discrete Event Systems

Recently, we have introduced bi-fuzzy discrete event systems (BFDESs) and established their supervisory control theory under full observations and partial observations, respectively. Compared with the models of discrete event systems and fuzzy discrete event systems, BFDESs are more satisfactory models to characterize some high-uncertainty systems. In this paper, we study the fault diagnosis problems of BFDESs. First, the framework of state-based decentralized diagnosis is introduced. Then, the notion of state-based codiagnosability is defined and a necessary and sufficient condition for state-based codiagnosability is provided. In particular, a polynomial-time algorithm for state-based codiagnosability verification and an online decentralized diagnosis method are presented. In addition, a compact state-based decentralized diagnosis framework is introduced, and the notion of state-based jointly diagnosability and its verification algorithm are proposed. Finally, the implication relationships between the two diagnosabilities are investigated.