Résumé
This paper presents an optimal control strategy allowing the maximization of the total production of a membrane filtration system over a finite time horizon. A simple mathematical model of membrane fouling is used to capture the dynamic behavior of the process which consists in the attachment of matter onto the membrane during the filtration period and the detachment of matter during the cleaning period. The control variable is the sequence of filtration/relaxation cycles over the time. Based on the maximum principle, we provide an optimal control strategy involving a singular arc and a switching curve. The proposed optimal control strategy is then compared to a classical control sequence published in the literature.