Optimal periodic control for scalar dynamics under integral constraint on the input - Application to the chemostat model

Térence Bayen (1) , Alain Rapaport (2) , Fatima-Zahra Tani (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie

This paper studies a periodic optimal control problem governed by a one-dimensional system, linear with respect to the control u, under an integral constraint on u. We give conditions for which the value of the cost function at steady state with a constant control U can be improved by considering periodic control u with average value equal to U. This leads to the so-called " over-yielding " met in several applications. With the use of the Pontryagin Maximum Principle, we provide the optimal synthesis of periodic strategies under the integral constraint. The results are illustrated on a problem of water quality in the chemostat model with periodic dilution rate, for various growth functions.

Mots clés: Key-Words Optimal Control; Pontryagin Maximum Principle; Periodic solutions; Chemostat Model; Over-yielding

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Térence Bayen, Alain Rapaport, Fatima-Zahra Tani. Optimal periodic control for scalar dynamics under integral constraint on the input - Application to the chemostat model . 2018. ⟨hal-01700128v1⟩