Abstract The aim of this paper is to investigate, via a case study, an adaptive extremum seeking control scheme for product formation in fed-batch bioreactors. The presented approach utilizes the structure information of the Haldane kinetic model, to derive an extremum seeking algorithm that drives the system to the desired set points with the objective to maximize the product formation rate. The adaptive extremum seeking algorithm consists of a control law and parameter learning laws designed by using Lyapunov's stability arguments. The adaptive extremum seeking control scheme is applied to the maximization of the enzyme production yield in filamentous fungal fermentation. Numerical simulations are provided in order to investigate the effectiveness of the proposed scheme.