Degrees of freedom approach to admissible feed-rate profiles for optimal fed-batch fermentation

Optimal feed-rate profiles for fed-batch fermentation are not easy to obtain, especially when the order of the process is high. Pontryagin's minimum principle (PMP) transforms the problem into a two-point boundary value problem (TPBVP).(1) The optimal feed-rate profile can be ascertained only numerically by calculating many potential solutions of the TPBVP with various necessary conditions and picking the one with the best performance index. Degrees of freedom (DF) analysis of TPBVP is useful in eliminating inadmissible feed-rate profiles and ensuring admissible feed-rate profiles, which can be incorporated into a computational scheme to obtain rapidly the optimal feed-rate profile.