Computation of admissible marking sets in weighted state machines by dynamic programming

In this paper we aim to characterize the admissible marking set in partially controllable Petri nets with weighted arcs. We consider a special subclass of generalized Petri nets called weighted state machines (WSMs) that have state-machine topology with weighted arcs. Such subclass of nets can be used to model systems of practical interest characterized by operations executed in batches. We propose a dynamic programming method to compute the admissible marking set of an elementary GMEC for a net in this subclass. Such a result can be used to design an online control logic to ensure that the current marking is always covered by some maximal admissible markings and is always admissible.