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利用Ｈｏｐｆｉｅｌｄ反馈神经网络对一类仿射非线性系统进行反馈线性化，然后利用常规的ＰＩ控制方法设计控制器．同时指出，利用神经网络不仅可以对系统的状态进行辨识，而且可以辨识其相对阶数，并给出了完整的证明．在训练神经网络时，提出了一种直接基于寻优参数的遗传算法ＤＰＧＡ，仿真结果说明了该线性化方法的有效性．
Hopfield feedback neural network is used to linearize a class of affine nonlinear systems, and then the controller is designed by the conventional PI control method. At the same time, it is pointed out that the use of neural network can not only identify the state of the system, but also identify its relative order, and give a complete proof. In the training of neural network, a genetic algorithm based on optimization parameters is proposed. The simulation results show the effectiveness of the linearization method.