Maximizing microalgae productivity by shading outdoor cultures

Outdoor microalgae cultures can undergo a photoinhibitory process that can result in a loss in biomass productivity. This loss can be reduced by shading the culture such that the incident photon flux decreases. Based on a simple model of light-limited growth, we look for a control strategy to shadow the culture in order to maximize the biomass productivity. The strategy results in a feedback control that depends on the microalgae strain, the microalgae concentration, and the incident light. In the case that the incident light and the loss rate vary periodically in time, we give conditions for the existence of a positive periodic solution that is globally stable. We show the performance of the feedback control by means of numerical simulations.