Optimal production of microalgae in the presence of grazers

Zooplankton contamination represents a major constraint in large-scale microalgal cultivation systems. While zooplankton contamination cannot be avoided, their development can be controlled by regulating the dilution rate. However, it is not straightforward to find the best control strategy for the dilution rate. Low dilution rates (or long retention times) favor grazer development and high dilution rates avoid their establishment at the risk of reducing microalgal productivity. Furthermore, the presence of periodic regimes arising from the interaction predator–prey makes it unclear if the presence of grazers must be completely avoided. In this paper, we study the role of the dilution rate in the control of zooplankton populations and in the optimization of biomass productivity. We show that in the long-term operation (static optimal control problem or SOCP), the optimal constant dilution rate must ensure the eradication of the zooplankton population. In the case of time-varying dilution rate, we numerically solve an optimal control problem (OCP) over a finite interval of time. We find that the optimal solution approaches the solution for the SOCP most of the time, except when zooplankton actively avoid the pond outflow. Based on these results, we propose a simple sub-optimal feedback control that approximately matches the solution of the OCP when the initial concentration of grazers is low.