Limitation of flow variation of Timed Continuous Petri Nets via Model Predictive Control and Lyapunov criterion

This paper addresses the problem of flow variation of Timed Continuous Petri Net (TCPN) systems under infinite server semantics. The problem is studied using Model Predictive Control. Our goal is to find an approach which limits the high flow variation by adding, in the cost function, a new term that takes in consideration these variations and that is pondered with a weighting factor. It has been shown that the weighting factor plays an important role in reducing the abrupt changes and therefore the excessive solicitation of the actuators. However, a large value of this factor leads to the occurrence of some oscillations due to a stability problem. Hence, Lyapunov criterion is applied to the cost function in order to find both the greatest value of the weighting factor for which the stability of the TCPN system is guaranteed and the control action which drives the system from an initial marking to a desired one and reduces the high flow variations. Consequently, the flow is smooth and the high flow variation is reduced.