Design of Optimal Control Sequences in Petri Nets Using Basis Marking Analysis

In this article, we develop an algorithm for designing an optimal control sequence in Petri nets, which drives a plant net from a source marking to a set of target markings without passing any pregiven forbidden markings. Such control sequences are useful in flexible reconfigurable automated systems, where a plant necessarily responds promptly to a request of reconfiguration. We develop a Dijkstra searching algorithm that is carried out in the basis marking space of a plant net instead of the conventional reachability space. Hence, only a small subset of the reachability set is explored, while the unpromising branches are reduced. Moreover, we propose a transition selecting rule to expose all forbidden trajectories and all first-met target markings during the searching process. The main advantage of the proposed method is wide applicability and low computational effort.