中文摘要：

神经网络应用于非线性建模具有很多优点,但对迟滞这类多值映射非线性无能为力。一个新的基于神经网络的迟滞建模方法——拓展空间法被提出。通过坐标变换建立基本迟滞算子,将基本迟滞算子的输出与迟滞输入同时作为神经网络的输入,使神经网络的输入空间由一维上升为二维,从而使输入与输出之间形成一对一映射关系。最后的实验结果表明,通过拓展空间法神经网络能够对多值映射非线性进行建模。

英文摘要：

There are many advantages of using neural network to model nonlinearity. But,it has been proven that the traditional approach of neural network cannot approximate multi-valued mapping. A new method modeling hysteresis,expanding-space method,was proposed. Continuous transformation was used to construct an elementary hysteresis operator （EHO）. The output of the EHO and the input of hysteresis were used as the input feds to the NN so that the input space of NN was expanded. The multi-valued mapping of hysteresis was transformed into one-to-one mapping. Finally,an experimental example of using the proposed modeling scheme was proposed. The result of the experiment indicates that neural network can approximate multi-valued mapping using expanding-space method.