A nonsingular optimization approach to the feed rate profile optimization of fedbatch cultures

A new method to calculate the optimal feed rate profile for fedbatch culture is proposed. Instead of the usual singular control approach of taking the feed rate as the control variable, the substrate concentration profile is used as the transformed control variable to avoid the computational difficulty associated with the singular control. Thus, the problem is converted into a nonsingular optimization problem of determining the optimal substrate concentration profile subject to a constraint. The equivalent feed rate profile to match the optimal substrate concentration profile is then generated. With this method the computational difficulty associated with singular controls for high-order systems is circumvented. The proposed method is illustrated by a number of examples.