A new approach for finding smooth optimal feeding profiles in fed-batch fermentations

•A proposal for obtaining smooth control profiles in fed-batch processes is given.•Proposal relies on parameterization of control vector by sinusoidal functions.•Sinusoidal based parameterization requires less number of parameters.•Application of proposed parameterization may avoid substrate shock in bioprocesses.•Approach leads to maximal productivity by using smooth-continuous feeding profiles.

In this work, a new approach for smooth control profiles parameterization (requiring a small number of parameters) is presented and especially recommended for bioprocess applications because of the smoothness of the profiles obtained, which are not only continuous time functions but also differentiable along the whole control interval. The importance of smooth profiles relays on the fact that abrupt changes in the cells’ environment may affect the metabolism of the cell, usually leading to a decrease in the process productivity. The parameterization proposed in this work is based on sinusoidal functions, which not only describe smooth functions but also are flexible and naturally constrained. Two very well-known bioprocess case studies have been successfully addressed by using the new parameterization approach.