Optimal and Sub-optimal Feedback Controls for Biogas Production

Antoine Haddon (1, 2) , Hector H. Ramirez (2) , Alain Rapaport (1)

1 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
2 DIM - Departamento de Ingeniera Matematica [Santiago]

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.

Mots clés: Singular arc; Chemostat model; Optimal control; Sub-optimality; Infinite horizon

Domaines: Optimisation et contrôle [math.OC]; Génie des procédés

Antoine Haddon, Hector H. Ramirez, Alain Rapaport. Optimal and Sub-optimal Feedback Controls for Biogas Production. Journal of Optimization Theory and Applications, 2019, 183 (2), pp.642-670. ⟨10.1007/s10957-019-01570-3⟩. ⟨hal-02165599⟩