Optimization of Microalgae Selection: Highlighting turnpike features

Abstract We consider a simplified dynamical system to represent the competition between two species of microalgae in a chemostat. The model is derived from the classical Droop model, assuming the substrate level can be directly controlled. An optimal control problem (OCP) is formulated, with the objective of finding the substrate concentration which would maximize the fraction of the species of interest over a fixed finite time-window. We characterize the substrate-based control strategy that steers the model trajectories and achieves species separation. Our objective is to highlight through a numerical optimal-synthesis - based on direct optimal control tools - the existence of a turnpike feature that appears in the optimal control law as well as in the optimal model trajectories and their co-states.