Fault Identification of Discrete Event Systems Modeled by Petri Nets With Unobservable Transitions

This paper deals with the identification problem of faulty behavior in a discrete event system, assuming that the fault-free model of a system is given in terms of Petri nets, where the set of transitions is divided into two disjoint subsets: 1) observable and 2) unobservable ones. The observed system output is defined as a transition-marking sequence, i.e., each transition is followed by a marking. First, a nonlinear integer programming model that characterizes the faults modeled by fault transitions is built according to the abnormal behavior extracted from the observed sequence. Then, it is converted into an integer linear programming (ILP) problem and a faulty net that preserves the structure of the fault-free one is obtained by solving this ILP model. In addition, an algorithm is developed to ensure acyclicity of the resulting unobservable subnet whose transition set is composed of the unobservable transitions of the fault-free net and the identified fault transitions.