Optimization of microalgae biosynthesis via controlled algal-bacterial symbiosis

TL;DR

This paper develops optimal control strategies for enhancing microalgae biomass production in a bioreactor by managing algal-bacterial interactions and resource allocation, demonstrating potential advantages of dynamic over static control methods.

Contribution

It introduces a novel optimal control framework for algal-bacterial consortia, analyzing static and dynamic solutions and their effectiveness in bioreactor optimization.

Findings

Dynamic control solutions include bang-bang and singular arcs.

Dynamic control can outperform static solutions in biomass maximization.

Convexity and uniqueness of static solutions are characterized.

Abstract

We investigate optimization of an algal-bacterial consortium, where an exogenous control input modulates bacterial resource allocation between growth and synthesis of a resource that is limiting for algal growth. Maximization of algal biomass synthesis is pursued in a continuous bioreactor, with dilution rate as an additional control variable. We formulate optimal control in the two variants of static and dynamic control problems, and address them by theoretical and numerical tools. We explore convexity of the static problem and uniqueness of its solution, and show that the dynamic problem displays a solution with bang-bang control actions and singular arcs that result in cyclic control actions. We finally discuss the relation among the two solutions and show the extent to which dynamic control can outperform static optimal solutions.