An Algorithm for Maximizing the Biogas Production in a Chemostat

Antoine Haddon () and Cristopher Hermosilla ()
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Antoine Haddon: Universidad de Chile
Cristopher Hermosilla: Universidad Técnica Federico Santa María

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 3, No 15, 1150-1170

Abstract: 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.

Keywords: Optimal control; Chemostat model; Pontryagin maximum principle; Hamilton–Jacobi–Bellman equations; Optimal synthesis; 49M05; 49J15; 93A30 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-019-01522-x

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