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This paper studies an optimal control problem related to membrane filtration processes. A simple mathematical model of membrane fouling is used to capture the dynamic behavior of the filtration process which consists in the attachment of matter onto the membrane during the filtration period and the detachment of matter during the cleaning period. We consider the maximization of the net production of a membrane filtration system (i.e. the filtrate) over a finite time horizon, where control variable is the sequence of filtration/backwashing cycles over the operation time of process. Based on the Pontryagin Maximum Principle, we characterize the optimal control strategy and show that it presents a singular arc. Moreover we prove the existence of an additional switching curve before reaching the terminal state, and also the possibility of having a dispersal curve as a locus where two different strategies are both optimal.

This work presents a general model for production-regeneration systems, alternating two functioning modes, the first one as a production process while the second one regenerates the process performances. Such systems are quite common in industry: they include for instance filtration/backwash of membranes, discharge/charge of accumulators. Basically, in these systems the sequence of production/regeneration over time cycles is the manipulating variable. A simple mathematical model involving a single explanatory "hidden variable" to capture the dynamic behavior of the process in both functioning modes is designed. Based on the Pontryagin's Maximum Principle, we characterize the optimal control strategy for a given criterion minimizing the energy consumption under a constraint on the performances.

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.

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According to the Center for Disease Control and Prevention (CDC), the coronavirus disease 2019, a respiratory viral illness linked to significant morbidity, mortality, production loss, and severe economic depression, was the third-largest cause of death in 2020. Respiratory viruses such as influenza, respiratory syncytial virus, SARS-CoV-2, and adenovirus, are among the most common causes of respiratory illness in humans, spreading as pandemics or epidemics throughout all continents. Nanotechnologies are particles in the nanometer range made from various compositions. They can be lipid-based, polymer-based, protein-based, or inorganic in nature, but they are all bioinspired and virus-like. In this review, we aimed to present a short review of the different nanoparticles currently studied, in particular those which led to publications in the field of respiratory viruses. We evaluated those which could be beneficial for respiratory disease-based viruses; those which already have contributed, such as lipid nanoparticles in the context of COVID-19; and those which will contribute in the future either as vaccines or antiviral drug delivery systems. We present a short assessment based on a critical selection of evidence indicating nanotechnology’s promise in the prevention and treatment of respiratory infections.