Optimal Darwinian Selection of Microorganisms with Internal Storage

In this paper, we investigate the problem of species separation in minimal time. Droop model is considered to describe the evolution of two distinct populations of microorganisms that are in competition for the same resource in a photobioreactor. We focus on an optimal control problem (OCP) subject to a five-dimensional controlled system in which the control represents the dilution rate of the chemostat. The objective is to select the desired species in minimal-time and to synthesize an optimal feedback control. This is a very challenging issue, since we are are dealing with a ten-dimensional optimality system. We provide properties of optimal controls allowing the strain of interest to dominate the population. Our analysis is based on the Pontryagin Maximum Principle (PMP), along with a thorough study of singular arcs that is crucial in the synthesis of optimal controls. These theoretical results are also extensively illustrated and validated using a direct method in optimal control (via the Bocop software for numerically solving optimal control problems). The approach is illustrated with numerical examples with microalgae, reflecting the complexity of the optimal control structure and the richness of the dynamical behavior.

Automated summary

This paper investigates the problem of species separation in minimal time. The evolution of two competing microorganism populations for the same resource is described using the Droop model. The paper focuses on solving an optimal control problem subject to a controlled system with five dimensions. The objective is to select the desired species in minimal time and synthesize an optimal feedback control. The paper provides properties of optimal controls and utilizes the Pontryagin Maximum Principle and a study of singular arcs for analysis. The theoretical results are validated using numerical examples with microalgae and a direct method in optimal control.