Addressing the control problem of algae growth in water reservoirs with advanced dynamic optimization approaches

Abstract

In this work, we develop a lake eutrophication model to determine restoration policies for water quality improvement. This hybrid biogeochemical model has been formulated within a simultaneous dynamic optimization framework as an optimal control problem, whose solution provides limiting nutrient inflow profiles to the lake, as well as in-lake biomanipulation profiles. The water quality model comprises a set of partial differential algebraic equations in time and space, which result from dynamic mass balances on main phytoplankton groups, nutrients, dissolved oxygen and biochemical demand of oxygen. Spatial discretization has been performed in two layers. The simultaneous approach proceeds by discretizing control and state variables by collocation over finite elements and solving the large scale nonlinear program with an interior point method with successive quadratic programming techniques.