Three kinds of coprognosability for partially-observed discrete event systems via a matrix approach

Abstract Due to the important application in security and safety analysis, fault prognosis of discrete event systems (DESs) plays a more vital role in study of Cyber–physical systems. In this work, we study the problem of decentralized fault prognosis in the context of partially-observed DESs. Different from existing results, we establish algebraic structures of given systems under decentralized agents by semi-tensor product rather than observers or verifiers based on formal language methods. The structure matrices of decentralized partially-observed DESs are polynomial in the size of a given system and linear about the number of agents. Besides, combining the formal method and algebraic state space approach, we discuss three kinds of coprognosability, called ( M , K ) -disjunctive-coprognosability aiming at disjunctive architectures, ( M , K ) -conjunctive-coprognosability for conjunctive architectures and ( M , K ) -strongly-coprognosability focusing on general structures, respectively. Here, ( M , K ) is the performance bound of a given prognostic system. In order to take both fault prediction and isolation into consideration, the decentralized prognoser is required to issue the “ j ” alarm for the j th type of fault and “ 0 ” means no fault alarm. Meanwhile, we propose a polynomial-time algorithm to verify each kind of coprognosability based on the structure matrix approach and show that each verification is not separate.