Optimal control of a bioreactor for biofuel production
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.
Keywords
Cite
@article{arxiv.1303.6688,
title = {Optimal control of a bioreactor for biofuel production},
author = {Roberta Ghezzi and Benedetto Piccoli},
journal= {arXiv preprint arXiv:1303.6688},
year = {2015}
}
Comments
Changes with respect to version 1. Section 3 is split into two subsections: 3.1 where the single-input model is studied and section 3.2 where a unified multi-input model including three controls (glucose, xylose, oxygen concentrations) is studied with consequent improvement of Theorem 1. Section 4 compares results obtained with previous literature