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This paper is about trajectory tracking for discrete event systems. The main contribution is to compute incrementally control sequences with minimal or near-minimal length based on a partial exploration of the Petri net (PN) reachability graph and inspired by the model predictive control approach. The method is suitable for bounded and unbounded PNs, for PNs with weighted arcs and with some uncontrollable transitions. Finally forbidden markings or regions of markings are easily avoided with the proposed approach that can be used for supervisory control issues.