Theoretical and numerical analysis of an optimal control problem related to wastewater treatment

In this work we deal with the design and management of wastewater treatment systems, mainly the disposal of sea outfalls discharging polluting effluent from a sewerage system. This problem is formulated as a pointwise optimal control problem with state and control constraints. The main difficulties arise from the lack of regularity of the second member in the state system and from the pointwise constraints on the state variables. We develop the theoretical analysis of the problem, we propose an algorithm for its numerical resolution, and finally, we give results for a realistic problem posed in the ria of Vigo, Spain.