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Pré-Publication, Document De Travail Année : 2021

Optimal control of a two-species bioproducing microbial consortium

Résumé

We study the optimal control of a system of nonlinear ordinary differential equations modeling microbial populations with light-inducable genetic differentiation that generates a two-species microbial consortium relevant for bioproduction. Appealing to Pontryagin's maximum principle, we find different optimal control structures within different regions of the parameter space. Explicit solutions are obtained in a subset of parameter space, while, for the remainder of parameter space, closed-form solutions are obtained that depend on a scalar value that solves a particular transcendental equation. We show that a unique solution of the scalar equation exists and lies in a known compact interval, making its numerical approximation particularly easy. The analytical results are verified against direct numerical calculations.
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Dates et versions

hal-03479385 , version 1 (14-12-2021)
hal-03479385 , version 2 (21-06-2022)

Identifiants

  • HAL Id : hal-03479385 , version 1

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Davin Lunz, J Frédéric Bonnans. Optimal control of a two-species bioproducing microbial consortium. 2021. ⟨hal-03479385v1⟩
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