State estimation in labeled time Petri net systems using observed modified state class graph

Abstract

In this paper, we present an improved method for the state estimation of a labeled time Petri net (LTPN) system with unobservable transitions. Precisely, we provide a computationally efficient graph, called an observed modified state class graph (OMSCG), that represents a partial state space of an LTPN system based on the logic label sequence of an observed time-label sequence (TLS), motivated by the modified state class graph reported in the literature. Taking advantage of the OMSCG, we can effectively estimate all the transition sequences that are logically consistent with a TLS. By employing the transitions-related timing constraints of the OMSCG, we then present an approach to determine the set of transition sequences that are timing consistent with a timed observation (i.e., a TLS observed at a time instant) by solving linear programming problems. Finally, we provide an algorithm to implement the state estimation of an LTPN system under a timed observation.