Optimal Feed Trajectories for Fedbatch Fermentation with Substrate Inhibition Kinetics

Abstract We provide optimal feed trajectories for fedbatch fermentation of microorganisms with substrate inhibition kinetics. We demonstrate that the optimal trajectories are non-unique and provide analytical procedures for solving the optimal control problem. Since, the optimal trajectories are non-unique this is essential for practical operations as a numerical solution could be any of the feasible non-unique optimal solutions. In addition, we investigate the sensitivity of the optimal trajectories and demonstrate that a bang-bang solution is optimal from a sensitivity point of view. This insight is relevant for model predictive control of fedbatch fermentation.