Fault model identification and synthesis in Petri nets

Fault identification studies in the Discrete Event Systems literature are typically model-based and require knowledge of the structure of the system, including the nature (and behavior) of the possible faults. In this paper we consider this problem within the framework of Petri nets assuming knowledge of the nominal (fault-free) system model but removing the requirement that the nature (or behavior) of the faults is known. Specifically, we consider a setting where faults are unobservable and use sequences of observations to infer the structure and behavior of faults. The resulting method recognizes the structure of the faulty system using knowledge of the structure of the fault-free system, and the projection of the faulty system language on the set of non-faulty events, which are assumed to be observable. Two problem formulations can be given: (i) fault identification when the resulting faulty Petri net system is required to generate all observed sequences, while no constraint is imposed on sequences that are not observed; (ii) fault synthesis where the resulting faulty Petri net system is required to only generate all observed sequences, while all sequences that are not observed cannot actually occur. We show that a solution to the first problem can always be easily found, while the synthesis problem is not trivial at all and we solve it via an approach based on linear integer programming, which allows us to take into account physical constraints on the system in terms of possible and not possible interactions in the system.