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An Algorithm for Maximizing the Biogas Production in a Chemostat

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  • Antoine Haddon

    (Universidad de Chile
    MISTEA, Université Montpellier, INRA, Montpellier SupAgro)

  • Cristopher Hermosilla

    (Universidad Técnica Federico Santa María)

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.

Suggested Citation

  • Antoine Haddon & Cristopher Hermosilla, 2019. "An Algorithm for Maximizing the Biogas Production in a Chemostat," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1150-1170, September.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:3:d:10.1007_s10957-019-01522-x
    DOI: 10.1007/s10957-019-01522-x
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    References listed on IDEAS

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    1. Beddoes, Jenifer C. & Bracmort, Kelsi S. & Burns, Robert T. & Lazarus, William F., 2007. "An Analysis of Energy Production Costs from Anaerobic Digestion Systems on U.S. Livestock Production Facilities," USDA Miscellaneous 330474, United States Department of Agriculture.
    2. Terence Bayen & Olivier Cots & Pedro Gajardo, 2018. "Analysis of an Optimal Control Problem Related to the Anaerobic Digestion Process," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 627-659, August.
    3. Djatkov, Djordje & Effenberger, Mathias & Martinov, Milan, 2014. "Method for assessing and improving the efficiency of agricultural biogas plants based on fuzzy logic and expert systems," Applied Energy, Elsevier, vol. 134(C), pages 163-175.
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