Model Identification of Unobservable Behavior of Discrete Event Systems Using Petri Nets

Abstract

This paper deals with the problem of identifying a Petri net that models the unobservable behavior of a system from the knowledge of its dynamical evolution. We assume that a partial Petri net model that represents the observable behavior of a system is given in which all the transitions are observable. An identifier monitors the system evolution and records the observed transition sequence (and possible corresponding markings). Some unobservable transitions modeling the unknown system behavior are identified from the transition sequence by formulating and solving integer linear programming problems. These identified unobservable transitions together with the given partial Petri net model characterize the whole system, including observable and unobservable behavior. Two different cases are considered. First, we assume that no place is observable. In such a case, a transition sequence is observed only during the evolution of the system. Second, we assume that a subset of places is observable; i.e., the observation contains not only the transition sequence but the corresponding markings as well. Hence an additional constraint should be imposed on the unobservable transition in the related programming problems according to the observed markings such that a more authentic unobservable transition can be found.