Estimation of P-Time Labeled Petri Nets with unobservable transitions

This paper focuses on the problem of estimating the marking of a P-time labeled Petri net with partial information. The set of transitions is partitioned into those labeled with the empty string epsilon called silent, as their firing cannot be detected, and the observable ones. The proposed approach is based on the observation of transitions labels thanks to the synthesis of a state observer obtained from the behavior of the untimed underlying Petri net. A procedure that, given an observed word (sequence of labels defined over a given alphabet) with their occurrence dates, allows to determine the set of states consistent with the considered observation is provided, under the assumption of non-Zenoness of the subnet induced by the set of unobservable transitions. Furthermore, a source of nondeterminism is added as the case of indistinguishable transitions (transitions sharing the same label) is also considered. The method relies on the schedulability analysis of particular firing sequences, namely the candidates firing sequences and does not require the building of the state classes graph although the time is modeled as intervals.