非线性时滞系统的分析与辨识算法

Approaches to the Analysis and Identification of Hammerstein-Model Non-Linear Time-Delayed Systems

本文讨论由Hammerstein模型所描述的非线性系统的分析与辨识问题。该模型由一个无记忆非线性元件后接一个线性时滞环节组成,是描述非线性系统的一种基本模型形式。利用移位Chebyshev展开式,非线性系统状态方程可简化为一个线性代数矩阵方程,因而可借助数字计算机求解。通过将系统输入一状态输出观测数据展成移位Chebyshev级数,可利用最小二乘法估计出线性环节的未知参数和非线性元件的多项式系数。此外,本文所推导的方法还能有效地用来处理无时滞的非线性系统。文中给出了几个示例,从中可以看出该方法的精度和效果。

The analysis and identification of a non-linear system described by a Hammerstein model are discussed in this paper.The Hammerstein model,which consists of a zero-memory non-linear element fol- lowed by a linear time-delayed plant,is one of the basic models that describe a non-linear characteristic.By using the shifted Chebyshev expansion,a non-linear state equation is reduced to a linear alge- braic matrix equation,which can be solved by a digital computer. Through the shifted Chebyshev expansion of the input-output mea- surements of the non-linear system,unknown parameters of both the linear time-delayed plant and the polynomial approximation of the non-linear element are estimated in terms of least squares method. In addition,the approaches presented here can be also applied to non-linear systems without time delay by simply equating the appropriate terms to zero and the delay matrix to the identity. Illustrative examples are given to demonstrate the superiority and the accuracy of the approaches.