An Algorithm for Maximizing the Biogas Production in a Chemostat - INRAE - Institut national de recherche pour l’agriculture, l’alimentation et l’environnement Access content directly
Journal Articles Year : 2019

An Algorithm for Maximizing the Biogas Production in a Chemostat

Abstract

In this work, we deal with the optimal control problem of maximizing biogas production in a chemostat. The dilution rate is the controlled variable, and we study the problem over a fixed finite horizon, for positive initial conditions. We consider the single reaction model and work with a broad class of growth rate functions. With the Pontryagin maximum principle, we construct a one-parameter family of extremal controls of type bang-singular arc. The parameter of these extremal controls is the constant value of the Hamiltonian. Using the Hamilton–Jacobi–Bellman equation, we identify the optimal control as the extremal associated with the value of the Hamiltonian, which satisfies a fixed point equation. We then propose a numerical algorithm to compute the optimal control by solving this fixed point equation. We illustrate this method with the two major types of growth functions of Monod and Haldane.
Fichier principal
Vignette du fichier
2019-Haddon.pdf (477.83 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive

Dates and versions

hal-02617851 , version 1 (13-06-2022)

Licence

Attribution

Identifiers

Cite

Antoine Haddon, Cristopher Hermosilla. An Algorithm for Maximizing the Biogas Production in a Chemostat. 2019, 182 (3), pp.1150-1170. ⟨10.1007/s10957-019-01522-x⟩. ⟨hal-02617851⟩
34 View
72 Download

Altmetric

Share

Gmail Facebook X LinkedIn More