Systematic development of optimal control strategies for fed-batch fermentation processes is of particular interest to both biotechnology-related industries and academic researches [2,7,14], since it can improve the benefit/cost ratio both economically and environmentally. Many biotechnology-based products such as pharmaceutical products, agricultural products, specialty chemicals and biochemicals are made in fed-batch fermentations commercially. Fed-batch is generally superior to batch processing on the final yield. However, maintaining the correct balance between the feed rate and the respiratory capacity is a critical task. Overfeeding is detrimental to cell growth, while underfeeding of nutrients will cause starvation and thus reduce the production formation too. From the process engineering point of view, it opens a challenging area to maximize the productivity by finding the optimal control profile.
In reality, to control a fed-batch fermentation at its optimal state is not straightforward as mentioned above. Several optimization techniques have been proposed in the literature . The conventional optimization methods that are based on mathematical optimization techniques are usually unable to work well for such systems . Pontryagin's maximum principle has been widely used to optimize penicillin production  and biphasic growth of Sac-charomyces Carlsbergensis . The mathematical models used in all these cases are of low-order systems, i.e., a fourth order system. However, it becomes difficult to apply Pontryagin's maximum principle if a system is of an order greater than five.
Dynamic programming (DP) algorithms have been used to determine the optimal profiles for hybridoma cultures [24,25]. For the fed-batch culture of hybridoma cells, more state variables are required to describe the culture since the cells grow on two main substrates, glucose and glutamine, and release toxic products, lactate and ammonia, in addition to the desired metabolites. This leads to a seventh order model for fed-batch operation, hence, it is difficult to apply Pontryagin's maximum principle. the DP is thus used to determine optimal trajectories for such high-order systems. However, the search space comprises all possible solutions to the high-order systems and is too large to be exhaustively searched. A huge computational effort is involved in this approach which sometimes may lead to a sub-optimal solution.
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