American Institute of Mathematical Sciences

June  2017, 7(2): 235-257. doi: 10.3934/mcrf.2017008

Optimal control of a multi-level dynamic model for biofuel production

 1 Institut de Mathématiques de Bourgogne, COMUE Université Bourgogne-Franche Comté, 9 Avenue Alain Savary, 21078 Dijon, France 2 Department of Mathematical Sciences and Center, for Computational and Integrative Biology, Rutgers University 311 N 5th St, 08102 Camden NJ, USA

* Corresponding author

Received  March 2016 Revised  October 2016 Published  April 2017

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. For the multi-input case, under suitable assumptions, we prove that generically with respect to initial conditions optimal controls are bang-bang. For the single-input case the result is even stronger as we show that optimal controls are bang-bang.

Citation: Roberta Ghezzi, Benedetto Piccoli. Optimal control of a multi-level dynamic model for biofuel production. Mathematical Control & Related Fields, 2017, 7 (2) : 235-257. doi: 10.3934/mcrf.2017008
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References:
Bioprocess scheme exhibiting full coupling between metabolic activity and external dynamics
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