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Optimal and Sub-optimal Feedback Controls for Biogas Production

Author

Listed:
  • Antoine Haddon

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

  • Héctor Ramírez

    (Universidad de Chile)

  • Alain Rapaport

    (MISTEA, Université Montpellier, INRA, Montpellier SupAgro)

Abstract

We revisit the optimal control problem of maximizing biogas production in continuous bio-processes in two directions: 1. over an infinite horizon, 2. with sub-optimal controllers independent of the time horizon. For the first point, we identify a set of optimal controls for the problems with an averaged reward and with a discounted reward when the discount factor goes to 0 and we show that the value functions of both problems are equal. For the finite horizon problem, our approach relies on a framing of the value function by considering a different reward for which the optimal solution has an explicit optimal feedback that is time-independent. In particular, we show that this technique allows us to provide explicit bounds on the sub-optimality of the proposed controllers. The various strategies are finally illustrated on Haldane and Contois growth functions.

Suggested Citation

  • Antoine Haddon & Héctor Ramírez & Alain Rapaport, 2019. "Optimal and Sub-optimal Feedback Controls for Biogas Production," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 642-670, November.
    • Handle: RePEc:spr:joptap:v:183:y:2019:i:2:d:10.1007_s10957-019-01570-3
    DOI: 10.1007/s10957-019-01570-3
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    References listed on IDEAS

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    1. A. Rapaport & P. Cartigny, 2007. "Nonturnpike Optimal Solutions and Their Approximations in Infinite Horizon," Journal of Optimization Theory and Applications, Springer, vol. 134(1), pages 1-14, July.
    2. A. Rapaport & P. Cartigny, 2005. "Competition between Most Rapid Approach Paths: Necessary and Sufficient Conditions," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 1-27, January.
    3. Lars Grüne & Christopher M. Kellett & Steven R. Weller, 2017. "On the Relation Between Turnpike Properties for Finite and Infinite Horizon Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 727-745, June.
    Full references (including those not matched with items on IDEAS)

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    1. A. Rapaport & P. Cartigny, 2007. "Nonturnpike Optimal Solutions and Their Approximations in Infinite Horizon," Journal of Optimization Theory and Applications, Springer, vol. 134(1), pages 1-14, July.
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