Minimum-time flow control of timed continuous Choice-Free nets

This paper addresses the problem of reaching (and then maintaining) an (optimal) flow of timed continuous Choice-Free Petri nets in minimum-time. First, we compute the optimal flow by solving a linear programming problem. Then we focus on driving the system to a steady-state (marking) corresponding to the optimal flow. The main challenge of solving this problem is the fact that, in general, the steady-state marking corresponding to a given optimal flow is not unique. We propose a heuristic algorithm, in which at each time step we estimate a “best” firing count vector that drives the system to the convex region where the optimal flow is obtained; then an ON/OFF strategy is applied. Later, we show that some additional firings can further decrease the time spent to obtain the optimal flow.