基于核函数的系统模型辨识

本文提出一种基于核函数的系统模型辨识方法。首先通过线性最小二乘确定低维空间中的非线性子空间,并经主分量分析提取与线性子空间基向量近似正交的非线性主分量,再经核密度估计进行聚类,自适应选择多个核将非线性子空间映射到高维空间,从而将任何一个线性和非线性的联合问题最终变成一个高维空间中的线性问题,最后借助线性最小二乘获得一个精确参数的系统模型。经过实验验证,该方法具有较好的效果。

System Model Identification Based on Kernel Function

This paper presents a system model identification approach based on kernel function.The nonlinear subspace of low di- mension system space and its nonlinear principal components are abstracted in turns use of linear least square and PCA,and the latter which are orthogonal to base vectors of linear subspace are clustered through estimation of density,then being mapped form the nonlinear subspace of low dimensions into high dimension space by adaptively selecting several kernels,thus a problem consisted of linear and non- linear parts can be transformed into a linear one of high-dimension space.And a precise parameters model is got by use of least square adaptively.Finally,good experiments results are performed.