Marking observer in labeled petri nets with application to supervisory control

In this paper, we consider the problem of marking estimation in labeled Petri nets whose initial marking is known to belong to a given convex set, in the presence of silent transitions (i.e., transitions labeled with the empty word) and indistinguishable transitions (i.e., transitions sharing the same label with other transitions). First, 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); subsequently, this observation is used to construct (offline) a marking observer under appropriate boundedness assumptions. Using the marking observer we show how to derive, at design time, a state feedback control law under the assumption that all transitions sharing a label can be enabled or disabled simultaneously as a group; this way, the most burdensome part of the computations is performed offline.