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Many fed-batch processes can be considered as a class of control-affine nonlinear systems. In this paper, a new methodology of neural networks, called the Control Affine Feedforward Neural Network (CAFNN), is proposed. It can be trained easily. For constrained nonlinear optimization problems, it offers an effective and simple optimal control strategy by sequential quadratic programming in which the analytic gradient information can be computed directly. The proposed modeling and optimal control schemes are illustrated on an ethanol fermentation process. Compared with a general multilayer neural network, the nonlinear programming problem based on a CAFNN model is solved more accurately and efficiently.