Optimal control of a bioreactor for biofuel production

TL;DR

This paper formulates the dynamic flux balance analysis of bioreactors as an optimal control problem, analyzing control strategies and proving bang-bang control properties for biofuel production optimization.

Contribution

It introduces a hybrid optimal control framework for bioreactors, linking macroscopic and microscopic dynamics, and characterizes optimal controls as bang-bang under various conditions.

Findings

Optimal controls are bang-bang for single-input cases.

For multi-input cases, optimal controls are generically bang-bang.

Necessary conditions are derived using Pontryagin Maximum Principle.

Abstract

Dynamic flux balance analysis of a bioreactor is based on the coupling between a dynamic problem, which models the evolution of biomass, feeding substrates and metabolites, and a linear program, which encodes the metabolic activity inside cells. We cast the problem in the language of optimal control and propose a hybrid formulation to model the full coupling between macroscopic and microscopic level. On a given location of the hybrid system we analyze necessary conditions given by the Pontryagin Maximum Principle and discuss the presence of singular arcs. In particular, for the single-input case we prove that optimal controls are bang-bang. For the multi-input case, under suitable assumptions, we prove that generically with respect to initial conditions optimal controls are bang-bang.