A Geometrical Approach for the Optimal Control of Sequencing Batch Bio-Reactors

In this work, we consider an optimal control problem of a biological sequencing batch reactor (SBR) for the treatment of pollutants in wastewater. This model includes two biological reactions, one being aerobic while the other is anoxic. The objective is to find an optimal oxygen-injecting strategy to reach, in minimal time and in a minimal time/energy compromise, a target where the pollutants concentrations must fulfill normative constraints. Using a geometrical approach, we solve a more general optimal control problem and thanks to Pontryagin's Maximum Principle, we explicitly give the complete optimal strategy.