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.

由于在安全和安全分析中的重要应用，离散事件系统（DES）的故障预测在信息物理系统的研究中起着更重要的作用。在这项工作中，我们研究了部分观测 DES 背景下的分散故障预测问题。与现有结果不同，我们通过半张量积而不是基于形式语言方法的观察者或验证者在分散代理下建立给定系统的代数结构。分散的部分观测 DES 的结构矩阵在给定系统的大小上是多项式的，并且与代理的数量成线性关系。此外，结合形式方法和代数状态空间方法，我们讨论了三种可预测性，称为$(米,钾)$-针对分离式架构的分离式可预测性， $(米,钾)$- 联合架构的联合预测性和 $(米,钾)$- 强可预测性分别侧重于一般结构。这里，$(米,钾)$是给定预测系统的性能界限。为了兼顾故障预测和隔离，分布式预测器需要发布“$j$”的警报 $j$th 类型的故障和“$0$”表示无故障报警。同时，我们提出了一种基于结构矩阵方法的多项式时间算法来验证每种可预测性，并表明每种验证不是分开的。