IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v178y2018i2d10.1007_s10957-018-1292-7.html
   My bibliography  Save this article

Analysis of an Optimal Control Problem Related to the Anaerobic Digestion Process

Author

Listed:
  • Terence Bayen

    (Univ Montpellier, CNRS
    Univ Montpellier, INRA, Montpellier SupAgro)

  • Olivier Cots

    (INP-ENSEEIHT, IRIT and CNRS)

  • Pedro Gajardo

    (Universidad Técnica Federico Santa María)

Abstract

Our aim in this work is to synthesize optimal feeding strategies that maximize, over a time period, the biogas production in a continuously filled bioreactor controlled by its dilution rate. Such an anaerobic process is described by a four-dimensional dynamical system. Instead of modeling the optimization of the biogas production as a Lagrange-type optimal control problem, we propose a slightly different optimal control approach in this paper: We study the minimal time control problem to reach a target point, which is chosen in such a way that it maximizes the biogas production at steady state. Thanks to the Pontryagin maximum principle and the geometric control theory, we provide an optimal feedback control for the minimal time control problem, when the initial conditions are taken within the invariant and attractive manifold of the system. The optimal synthesis exhibits turnpike and anti-turnpike singular arcs and a cut locus.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:2:d:10.1007_s10957-018-1292-7
    DOI: 10.1007/s10957-018-1292-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-018-1292-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-018-1292-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:178:y:2018:i:2:d:10.1007_s10957-018-1292-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.