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In this paper we propose a new algorithm to approximate the solution of Hamilton-Jacobi-Bellman equation by using a three layer neural network for affine and general nonlinear systems, and the state feedback controller can be obtained which make the closed-loop systems be suboptimal within a restrictive training domain. Matrix calculus theory is used to get the gradients of training error with respect to the weight parameter matrices in neural networks. By using pattern mode learning algorithm, many examples show the effectiveness of the proposed method.