2013/03/26 by Roberta Ghezzi, Ghezzi, Roberta, Benedetto Piccoli +1
Biochemistry, Genetics and Molecular Biology · Engineering · #Advanced Control Systems Optimization #Biofuel production and bioconversion #FOS: Mathematics #Microbial Metabolic Engineering and Bioproduction #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1303.6688
openalex publication_date 2013/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.