An Algorithm for Maximizing the Biogas Production in a Chemostat
Author
dc.contributor.author
Haddon, Antoine
Author
dc.contributor.author
Hermosilla, Cristopher
Admission date
dc.date.accessioned
2019-10-22T03:15:03Z
Available date
dc.date.available
2019-10-22T03:15:03Z
Publication date
dc.date.issued
2019
Cita de ítem
dc.identifier.citation
Journal of Optimization Theory and Applications, Volumen 182, Issue 3, 2019, Pages 1150-1170
Identifier
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15732878
Identifier
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00223239
Identifier
dc.identifier.other
10.1007/s10957-019-01522-x
Identifier
dc.identifier.uri
https://repositorio.uchile.cl/handle/2250/172072
Abstract
dc.description.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.