Approaching minimum time control of timed continuous Petri nets

This paper considers the problem of controlling timed continuous Petri nets under infinite server semantics. The proposed control strategy assigns piecewise constant flows to transitions in order to reach the target state. First, by using linear programming, a method driving the system from the initial to the target state through a linear trajectory is developed. Then, in order to improve the time of the trajectory, intermediate states are added by means of bilinear programming. Finally, in order to handle potential perturbations, we develop a closed loop control strategy that follows the trajectory computed by the open loop control by calculating a new state after each time step. The algorithms developed here are applied to a manufacturing system.