The optimal control algorithm to calculate the optimal feed rate pro®le of nutrient solution containing two limiting nutrients was proposed. Different from other conventional optimization methods, the proposed algorithm calculated the optimal control pro®les for different initial and feed conditions. The singular optimal control algorithm, dynamic programming, and nonsingular transformation algorithm were used for the optimization of simple problems of the 4th order and the performances were compared. With the proposed transformation algorithm, the ®nal MAb concentration increased and the CPU time decreased.For the different initial glucose and glutamine conditions, the optimal control pro®les were calculated with the proposed transformation algorithm. As the initial glutamine concentration increased, the ®nal MAb concentration also increased due to the cell viability increase. This was also applied to the different feed compositions. When the glutamine concentration was increased in the feed stream, the ®nal MAb concentration also increased.

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