Diagnosability of composite automata based on semi-tensor product

Abstract

Fault diagnosis is an important issue of partially observed discrete event systems (DESs). In this problem, fault detection and isolation are two associated tasks, where a fault is diagnosable if it can be detected certainly with a finite delay occurrence and a system is diagnosable if any type of faults can be distinguished with the observed information. Existing researches for fault diagnosis tend to regard faults as unobservable faulty events or states. In this paper, there exists a key conversion, denoting faults by accessible changes of state transition, and then obtains a normative and a faulty construction of given systems. Specially, we establish algebraic structures of composite automata with the help of semi-tensor product and propose a definition of diagnosability based on algebraic state space. Notice that the definition is so different from existing results that provide a new opportunity to fault diagnosis when existing criteria fail. Besides, we construct matrix observers to summarize the requisite information in the evolutionary process and present corresponding theorems to the verification of diagnosability. We apply the exhaust gas recirculation system and the heating system to illustrate the matrix approach in this paper is feasible.