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Journal of Optimization Theory and Applications

, Volume 183, Issue 2, pp 642–670 | Cite as

Optimal and Sub-optimal Feedback Controls for Biogas Production

  • Antoine HaddonEmail author
  • Héctor Ramírez
  • Alain Rapaport
Article
  • 63 Downloads

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.

Keywords

Optimal control Chemostat model Singular arc Sub-optimality Infinite horizon 

Mathematics Subject Classification

49K15 49N35 49N90 93B52 

Notes

Acknowledgements

The first and second authors were supported by FONDECYT grants 1160567 and 1160204 and by Basal Program CMM-AFB 170001 from CONICYT, Chile. The first author was supported by a doctoral fellowship CONICYT-PFCHA/Doctorado Nacional/2017-21170249. The third author was supported by the LabEx NUMEV incorporated into the I-Site MUSE.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mathematical Engineering Department and Center for Mathematical Modelling (CNRS UMI 2807)Universidad de ChileSantiagoChile
  2. 2.MISTEA, Université Montpellier, INRA, Montpellier SupAgroMontpellierFrance

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