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Optimal control of a multi-level dynamic model 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. 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.
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Soumis le : mardi 4 juillet 2017 - 13:22:45
Dernière modification le : vendredi 25 novembre 2022 - 10:12:06

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Roberta Ghezzi, Benedetto Piccoli. Optimal control of a multi-level dynamic model for biofuel production. Mathematical Control and Related Fields, 2017, 7 (2), pp.235 - 257. ⟨10.3934/mcrf.2017008⟩. ⟨hal-01555738⟩



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