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.
Domaines
Optimisation et contrôle [math.OC]Origine | Fichiers produits par l'(les) auteur(s) |
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