Near-optimal control sequence design for untimed Petri nets based on a reduced breadth and depth exploration

This paper proposes algorithms to design control sequences for untimed Petri nets. The aim of the controller is to incrementally compute sequences of transition firings with minimal or near-minimal size from an initial marking to a reference one, avoiding forbidden markings and non-promising branches. The approach combines a partial exploration of the reachability graph with a model predictive control strategy. The main contribution is to explore only a small area of the reachability graph according to a double limitation in breadth and in depth in order to provide solution with a low computational effort. Thanks to its reduced computational effort and to the good performance of model predictive control in uncertain and perturbed environments, the method is suitable for proactive deadlock-free scheduling problems. It is applicable to a large class of discrete event systems in particular in the domain of flexible manufacturing, communication and computer science or transportation and traffic.