State Estimation of Timed Labeled Petri Nets With Unobservable Transitions

The aim of this paper is to reconstruct the least/greatest sequence of unobservable transitions in timed Petri nets based on the online observation of firing occurrences of some transitions on a sliding horizon. The Petri net, which can be unbounded and can contain self-loops and circuits, is described under an algebraic form composed of A.x ≤ b which expresses the possible time sequence x and the fundamental marking relation. Under the assumption of Backward/Forward Conflict Freeness of the unobservable-induced subnet, we show the existence of a finite least/greatest sequence with respect to the data known on a given horizon. A technique of computation using linear programming is given.