Optimal control of a bioreactor for biofuel production

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...

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Bibliographic Details
Published in:arXiv.org 2015-07
Main Authors: Ghezzi, Roberta, Piccoli, Benedetto
Format: Article
Language:English
Subjects:
Bioreactors
Coupling
Hybrid systems
Initial conditions
Maximum principle
Metabolites
Optimal control
Substrates
Online Access:Get full text
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Summary: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.
ISSN:2331-8422