Fourier-Motzkin method for failure diagnosis in Petri Net models of discrete event systems

This paper presents a new technique for failure diagnosis in partially observable discrete event systems modelled as Petri nets. In this new technique we adopt Integer Fourier-Motzkin Elimination (IFME) method. We start with a Petri net and produce the state equations. The state equations are a set of integer valued inequalities in variables that represent number of firing of transitions. Occurrences of failure can also be expressed by inequalities. Then we extend the set of inequalities obtained from the state equations to two new sets. The first is created from adding the inequality for failure. The second is created from adding the negation of the inequality for failure. Applying the IFME method to the two resulting sets of inequalities, the variables corresponding to unobservable transitions will be eliminated. Then we prove that for acyclic Petri nets, the reduced set of inequalities after the elimination can be used to diagnose failures.