Online fault diagnosis in Petri net models of discrete-event systems using Fourier-Motzkin

This paper presents a new approach for the fault diagnosis problem in partially observable discrete-event systems modelled with Petri nets. Our approach is based on the use of the Integer Fourier-Motzkin Elimination (IFME) method. The fault diagnosis problem is solved by first creating an initial set of inequalities from the state equation of a Petri net. The occurrence or absence of faults can also be expressed by inequalities. After adding these inequalities to the initial set, we apply the IFME method to eliminate the variables corresponding to unobservable transitions. The resulting set of inequalities is used for the purpose of diagnosis. We prove the correctness of our approach for both bounded and unbounded Petri nets with no cycles of unobservable transitions.