(untitled) (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 2021)
This paper studies the dynamics of a nonlinear control system, modelling an anaerobic wastewater treatment process. Under suitable assumption we regulate the biological oxygen demand so that its values fall between prescribed bounds. Since the biological and the chemical oxygen demand are strongly related, this allows us to regulate the pollution concentration according to existing ecological norms. The regulation is done in the following manner: We fix bounds for the values of the control function (the dilution rate) and show that the values of the biological oxygen demand of the corresponding dynamics tend to a prescribed interval as time tends to infinity. We also present a variety of numerical simulations using randomly chosen admissible controls in order to illustrate the robustness of the obtained results.