Marking Estimation of P-Time Petri Nets With Unobservable Transitions

This paper focuses on the problem of estimating the marking of an unlabeled P-time Petri net with partial information modeled by unobservable transitions. The proposed approach is based on a novel state observer synthesis method under partial observation. A procedure that, given a sequence of observable transitions with their firing time instants, allows to determine the set of markings consistent with the considered observation is given. The method relies on the feasibility in time (called schedulability) of particular firing sequences, namely the candidates firing sequences. Moreover, although time is taken into consideration, the proposed technique is not hampered by the state space explosion problem as it relies on the underlying untimed structure of the P-time model considered-the building of the state class graph is not necessary.