Résumé
Our aim in this work is to study the problem of driving in minimal time a system describing a chemostat model to a target point. This problem finds applications typically in the case where the input substrate concentration changes yielding in a new steady state. One essential feature is that the system takes into account a recirculation of biomass effect. We depict an optimal synthesis and provide an optimal feedback control of the problem by using the Pontryagin Maximum Principle and geometric control theory for both Monod and Haldane kinetics.