Three-dimensional nonlinear optimal control model of wastewater biotreatment

Abstract

Biological treatment of waste water involves bacteria, which remove waste products from the treated water and kill pathogens. Thus, this problem is closely linked to both the population dynamics and chemical kinetics. Aerobic process is very efficient but rather costly, as it requires aeration of the treated water. An aim of this paper is to explore the possibility to apply the ideas and methods of the optimal control theory to the problem of optimizing the costs of this process. In this paper, we consider a three-dimensional nonlinear model of water treatment with includes a bounded control. In order to foretell possible outcomes of the control, we analytically investigate the corresponding attainable set, constructing a parametric description of this set by moments of switching of piecewise constant controls. This allows us to visualize the attainable set using MATLAB. These results lead to a number of practically relevant conclusions.