Least-cost transition sequence estimation in labelled time Petri net systems with unobservable transitions

Abstract

This paper presents an approach to solve the least-cost transition sequences estimation problem in labelled time Petri net (LTPN) systems with unobservable transitions. Particularly, the considered LTPN system is bounded, in which each transition has a nonnegative cost and is labelled as either observable or unobservable. We first introduce a graph, called a segmented modified state class graph (SMSCG), that is a compact representation of the partial state space of an LTPN system. Based on the SMSCG and an observed time-label sequence, a method to estimate logic consistent transition sequences is proposed. By exploiting the transitions-related timing constraints in SMSCGs, a procedure for determining which logic consistent transition sequences are timing consistent with the observed time-label sequence and a given time is reported. Finally, we develop an algorithm to perform the estimation of least-cost transition sequences.