ON/OFF control for reaching a steady state attractive region in batches Petri nets

This paper addresses an event-driven control problem of controlled generalized batches Petri nets without discrete nodes, i.e., a class of hybrid Petri net formalisms. The goal of the controller is to reach a given steady state from an initial marking qualified as blocking, by controlling the flow of transitions. To this end, we firstly characterize an attractive region of the steady state as an optimal solution of a linear programming problem (LPP). Next, based on the ON/OFF state of transitions, which depends on the enabling conditions and the firing quantities, an ON/OFF event-driven control strategy is proposed for reaching, from a blocking initial marking quantity, the nearest marking quantity in the attractive region. The admissible controlled firing flow vector is computed according to a LPP which maximizes the firing flow of ON-transitions to its maximal firing flow while it imposes a null firing flow to OFF-transitions. The proposed strategy is event-driven and the control actions are updated only when specific events occur. The basic idea of this new control strategy is to fire each transition as fast as possible at any event step until the minimal firing quantity vector is reached.