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


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.


Optimal control Chemostat model Singular arc Sub-optimality Infinite horizon 

Mathematics Subject Classification

49K15 49N35 49N90 93B52 



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

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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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