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.

我们调查了化学杀虫剂模型的运行与定期控制生物水净化的好处。我们考虑的第一个问题是在一定时期内限制所处理水的总量的情况下使平均污染输出浓度最小化。第二个方法是在平均输出浓度的约束下使此数量最大化。我们首先给出微生物生长特性的条件，与稳态下的值相比，可以改善目标函数（针对两个问题）。然后，我们为第一个问题提供（全局）最优周期控制策略，然后我们展示两个问题的对偶性质，这使我们能够从第一个问题的解决方案中得出第二个问题的解决方案。