On State Estimation of Timed Petri Nets

In this paper, we present an online algorithm for state estimation of timed choice-free Petri nets. We assume that the net structure and initial marking are known, and that the set of transitions is divided in observable and unobservable one. Given an observed word and assuming that the time durations associated to the unobservable transitions are unknown, our problem is to estimate the possible states in which the timed net system can be. This work extends the notion of basis markings defined for untimed Petri nets considering now the time information. We propose an online algorithm using three main steps: (1) wait for a new observation and compute the set of basis markings without considering the time; (2) update the set of time equations that contain the time restriction for the unobservable transitions; (3) update the set of basis markings removing the time-inconsistent markings. The extension of the algorithm to general nets is discussed, as well.