Abstract
We investigate the benefit of operating the chemostat model with periodic controls for biological water decontamination. The first problem that we consider is to minimize the average output concentration of pollution under a constraint on the total quantity of water treated over the period. The second one consists in maximizing this quantity under a constraint on the average output concentration. We first give conditions on the growth characteristics of micro-organisms for which an improvement of the objective function (for the two problems) is possible, compared to the value at steady-state. We then provide the (global) optimal periodic control strategies for the first problem, and we then show a duality property both problems, which allows us to deduce the solutions of the second problem from the solutions of the first one. Results are illustrated on Monod’s, Haldane’s, Hill’s, and Contois’s kinetics.
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