Maximization of metabolite in fed-batch cultures: Sufficient conditions for singular arc and optimal feed rate profiles

Fed-batch fermentation for maximization of metabolite production at a final time is normally a singular control problem. The singular optimal feed rate strategy depends on relative position of peaks in the specific rates of cell growth μ, substrate consumption σ and product formation π. Regions in which singular feed rates exist are identified and variation of substrate concentration in the singular region is elucidated. Sufficient conditions for the existence of a singular arc are developed, which can be incorporated into an efficient and stable computational scheme to obtain the optimal feed rate profiles.