Optimal and Sub-optimal Feedback Controls for Biogas Production
- 63 Downloads
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.
KeywordsOptimal control Chemostat model Singular arc Sub-optimality Infinite horizon
Mathematics Subject Classification49K15 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.
- 16.Harmand, J., Lobry, C., Rapaport, A., Sari, T.: Optimal Control in Bioprocesses: Pontryagin’s Maximum Principle in Practice. Wiley, Chemical Engineering Series, Chemostat and Bioprocesses Set 3, Hoboken (2019)Google Scholar
- 30.Khalil, H.K.: Nonlinear Systems. Prentice Hall, Upper Saddle River (1996)Google Scholar
- 33.Dal Maso, G.: An Introduction to \(\Gamma \)-convergence, vol. 8. Springer, New York (2012)Google Scholar