Marking Observer of Labeled Petri Nets with Uncertainty in the Initial Marking

In this paper we consider marking estimation in labeled Petri nets whose initial marking is known to belong to a given convex set. We allow for silent transitions (i.e., transitions labeled with the empty word) and indistinguishable transitions (i.e., transitions sharing the same label with other transitions). We demonstrate that all sets of markings consistent with a given sequence of observations can be described in linear algebraic terms (as a union of convex sets) and a marking observer may be constructed offline under appropriate bounded ness assumptions. This reduces the problem of computing the set of markings consistent with a given observation sequence to the problem of moving along a path in a labeled directed graph.