Estimation of Least-Cost Transition Firing Sequences in Labeled Petri Nets by Using Basis Reachability Graph

This paper develops an approach for solving the problem of least-cost transition firing sequences estimation in labeled Petri nets with unobservable transitions. Each transition in the net is labeled as either observable or unobservable, and has a nonnegative cost. Additionally, we assume that the net system is bounded, the unobservable subnet is acyclic, and the cost of each unobservable transition is strictly positive. We propose the method mainly on the basis of the notions of basis marking and basis reachability graph (BRG), which is a compact representation of the reachability graph of the net system. By sacrificing extra storage space to keep the BRG and other necessary information in memory, some time-consuming computations are moved off-line. This makes our proposed approach more feasible for on-line applications. Finally, we present a brief survey and comparison of some representative methods that use labeled Petri nets as a formalism in the literature.