Design of control sequences for timed Petri nets based on tree encoding

This paper concerns the design of optimal control sequences for timed Petri nets under earliest firing policy. Optimality is defined with respect to the sequences duration. A method inspired by model predictive control combined with a partial exploration of the reachability graphs of the logical net system underlying the timed PN model is proposed. The main contribution is to provide, under some assumptions, a suboptimal solution based on an approximation of the minimal duration of a feasible firing sequence when only its firing count vector is assumed to be known. This approximation is given as an interval to which the minimal duration necessarily belongs. For that purpose, a systematic tree encoding of the net structure is proposed.