State feedback control of labeled Petri nets with uncertainty in the initial marking

In this paper we consider the problem of designing a state feedback controller for a labeled Petri net 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). Transitions that are neither silent nor indistinguishable, are said to be observable since the observation of their label univocally identifies them. Moreover, we divide the set of observable transitions into controllable and uncontrollable (all unobservable transitions are obviously uncontrollable). Based on our previous results on marking observation in the above setting, we show how to derive, at design time, a state feedback control law; this way, the most burdensome part of the computations, is performed off-line.