Analysis of optimal control problems for the process of wastewater biological treatment

We consider a three-dimensional deterministic control model of the process of aerobic wastewater biotreatment. For this model, we formulate and solve two optimal control problems, each of which has a corresponding minimizing functional. For the first problem, the functional is a weighted sum of the...

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Main Authors: Grigorieva, Ellina V., Bondarenko, Natalia V., Khailov, Evgenii N., Korobeinikov, Andrei
Format: Artículo
Language: Inglés
Published: 2015
Online Access: http://revistas.ucr.ac.cr/index.php/matematica/article/view/11430
http://hdl.handle.net/10669/13029
Summary: We consider a three-dimensional deterministic control model of the process of aerobic wastewater biotreatment. For this model, we formulate and solve two optimal control problems, each of which has a corresponding minimizing functional. For the first problem, the functional is a weighted sum of the pollutant concentration at the end of a fixed time interval and the cumulative biomass con- centration over the interval. For the second problem, the functional is a weighted sum of the pollutant concentration at the end of the time interval and the cumulative oxygen and biomass concentra- tions over the interval. In order to solve these problems, we apply the Pontryagin Maximum Principle. The switching functions are analytically investigated and uniquely determine the type of the op- timal controls for the considered problems. Their properties allow the simplification of the optimal control problems to that of finite- dimensional constrained minimization. Numerical solutions of the optimal control problems are also provided.