Near-Optimal Scheduling for Petri Net Models With Forbidden Markings

This paper is about control design for discrete event systems modeled with Petri nets. It addresses the problems of reachability and of firing sequence design. The untimed and timed cases are successively studied by searching control sequences from an initial marking to a reference one with length or duration that approach the minimal value, avoiding forbidden states and nonpromising branches. The proposed algorithms are applicable to a large class of discrete event systems in particular in the domain of flexible manufacturing, engineering. To accelerate the computation and make robust the control strategy, only a small area of the reachability graph is worked out and an approach inspired from model predictive control is used. The approach is suitable for deadlock-free scheduling and fault-tolerant control problems.