Approaching Minimal Time Control Sequences for Timed Petri Nets

The main contribution of this note is to propose algorithms that incrementally compute control sequences that drive the marking of timed Petri nets from an initial value to a reference one with a duration that approaches the minimal duration. These algorithms are based on a partial exploration of the reachability graph that is inspired from model predictive control. They include perturbation rejection and forbidden marking avoidance and are suitable to track trajectories when the initial and reference markings are far from each other. Application cases illustrate the efficiency of the method.