Optimal Management of a Bioreactor for Eutrophicated Water Treatment: A Numerical Approach

This paper presents a numerical algorithm for computing the optimal design variables in the management of a bioreactor for the treatment of eutrophicated water: initial and distributed quantities of phytoplankton added along the process, and total duration of the process. This real-world problem is formulated as a state-control constrained optimal control problem, whose numerical resolution is the main aim of this study. After discretizing the control problem, we present a structured algorithm for solving the discrete state systems, computing the corresponding derivatives, and minimizing the objective function. Finally, the good performance of the algorithm is shown by applying it to a realistic example with two pre-reservoirs.

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