Limitation of flow variation of timed continuous Petri Nets via Model Predictive Control

This paper addresses the problem of flow variation of timed continuous Petri Nets under infinite server semantics. Our goal is not only to demonstrate the impact of the weighting factor associated to the expression of the flow in the cost function, in reducing flow variation. It is also to find the optimal value and a control optimizing the defined cost function that drives the evolution of the system from an initial marking M0 to a desired one Md and reduces the high flow variation. The problem is studied using Model Predictive Control (MPC). The variation rate is reduced significantly whereas some oscillations around the desired marking arise. The optimal weighting factor is determined in order to limit the oscillations amplitude. Therefore, the flow is the smoothest and accordingly the excessive solicitation of actuators can be reduced.