Résumé : Production of high-content fructo-oligosaccharides by fermentation in a fed-batch bioreactor is considered. The fed-batch scenario allows to reduce inhibition mechanisms caused by the presence of by-products, such as glucose, while maximizing biomass production. The determination of the feed flow rate profile that maximizes the concentration of fructo-oligosaccharides is performed by resorting to the maximum principle of Pontryagin. The optimization procedure takes into account inequality constraints on the state and control variables and allows the determination of the unspecified fermentation final time corresponding to maximal fructo-oligosaccharides content. The performance of the approach is demonstrated by simulations in the case of fructo-oligosaccharide production by Aspergillus sp.