Neuro-dynamic Optimal Control of a L-lysine Fed-batch Fermentation

In this paper is developed an optimal control of fermentation process of L-lysine production with the Neuro-dynamic programming theory. A approximation neural network is developed and the decision of the optimization problem is improved by an iteration mode founded on the Bellman equation. With this optimization procedure the quantity L-lysine productions is increased at the end of the process. Introduction The L-lysine is one of the irreplaceable amino acid whose contents in the animal protein is low, but in the plant, protein is relatively high (5). The most effective and the cheapest method for L-lysine production is microbiological method by direct fermentation. Important problem for this fermentation is synthesis of a quality optimal control that can rice the process effectiveness. The optimal control of this process usually depends on the presence of complex, non-linear dynamic model of the system because of this is difficult to realize to working-out of the problem, which is very important to practical realize (2). Neuro-dynamic programming (NDP) is a relatively new class of Dynamic Programming (DP) methods for control and further decision making under uncertainties (1, 2). These methods have the potential to deal with problems that for a long time were thought to be intractable due to either a large state space or the lack of an accurate model. The name NDP expresses the reliance of the methods on both DP and neural networks (NN) concepts. In this case, in the artificial intelligence community, from where the methods originated, the name reinforcement learning is also used. There has been a gradual realization reinforcement learning techniques can be fruitfully motivated and interpreted in terms of classical DP concepts such as value and policy iteration. Two fundamental DP algorithms, policy iteration and value iteration, are the starting points for the NDP methodology. A new policy is then defined by minimization of Bellman’s equation, where the optimal cost is replaced by the calculated scoring function, and the process repeats (1). The method is successfully applied for optimal control of fermentation processes in the last years, as the computing time was decreased about 2/3 times and the quantity of the desired products was increased (4). In this paper the optimal control of a fermentation process for L-lysine by Neuro-dynamic programming will be synthesized. Model of the Process In this paper а process for L-lysine production that is leaded in stirred tank bioreactor is examine. The model of the process has type: