Distributed Non-Concurrent Fault Identification in Discrete Event Systems

In this paper we study fault identification in discrete event systems that are described by Petri nets. We consider fault models that capture faults in both Petri net transitions and places and we assume that the system events are unobservable but the system state is periodically observable. Our approach employs redundant Petri net embeddings that are designed in a way that enables fault detection and identification to be performed in a centralized or distributed manner using algebraic decoding techniques. We first develop an efficient method for solving a system of composite power polynomial equations and then combine this method with traditional decoding techniques for Reed-Solomon codes in order to identify multiple transition and place faults using a centralized diagnosis mechanism. More specifically, using a redundant Petri net embedding with 2k additional places, we can simultaneously identify up to 2k 1 transition faults and up to k place faults (that may occur at various instants during the operation of the Petri net) with worst-case complexity of O(k2m + kn) operations (where m and n are respectively the number of transitions and places in the given Petri net model). The proposed diagnosis schemes are extended to distributed settings in ways that require negligible additional hardware.