Model Predictive Supervisory Control of Discrete Event Systems

Model predictive control is widely used in the process industry today. However, its application in fields where a discrete event system model is used, such as in manufacturing and logistics, remains limited. The state explosion problem represents a significant obstacle, which can be mitigated, when using Petri net models, adopting a basis marking representation of the reachability space. Specifically, the transition set of a Petri net is partitioned into subsets of explicit and implicit transitions. Controllable transitions are all included in the explicit transition set. The firing of implicit transitions can be abstracted, allowing the reachability set of the net to be completely characterized by a subset of reachable markings called basis markings. In this preliminary paper, based on the receding horizon approach, it is proposed to compute future supervisory control actions by considering the basis markings reached by firing explicit transitions along sequences of length equal to the prediction horizon specified by a positive integer.