神经网络控制结构确定方法

A New Method of Determination of Structure of Neural Network

为了选择合适的神经网络逼近不同的非线性函数，本文将该问题化为模型辨识问题来处理，并且给出了有效方法。为了确定样条函数、正交级数描述等神经网络阶次，本文提出了Ｕ—Ｄ分解的递阶数据矩阵法、递阶误差性能指标法等方法。

In this paper we discuss how to so select appropriate model and structure of neural network as to facilitate easy implementation and to exploit fully the ability of neural network to approximate an arbitrary nonlinear function abstracted from the object to be controlled. To our best knowledge, there does not as yet exist any method in the open literature for making such selection comparable in efficiency with the one proposed here. We convert the problem of selection of structure of neural network into a problem of model identification. DM (Data Matrix), CF (Cost Function), and WCF (Weighted Cost Function) are three well known methods of model identification. When we apply them to neural network, we modified them,and propose MDM, MCF, and MWDF methods. Our modification is essentially the use of U- D factorization and hierarchical technique. Thus, we derive eq. (4) for MDM, and eqs.(11) and (12) for MCF, and eqs. (15) and (16) for MWCF. MDM, MCF, and MWCF can ensure numerical stability and increase remarkably computational efficiency. Tables 1 and 2 show that, the larger the number of weighted coefficients is, the higher is the efficiency of MDM, MCF, and MWCF compared with other methods. The number of weighted coefficients is of course dependent on the complexity of neural network as required by the object to be controlled. Finally a numerical example is given. It does show that our modified methods are effective.