非线性系统的结构选择及其参数的集员辨识

Structure selection and parameter set-membership identification for nonlinear systems

基于支持向量回归和RBF(Radial Basis Function)神经网络,研究了带有未知但有界噪声的非线性系统的集员辨识问题.推导了噪声界以及支持向量个数与ε-不敏感参数之间的关系,给出了利用噪声界选择ε-不敏感参数的方法.描述了通过支持向量回归选择RBF神经网络规模的方法.该方法以Gaussian核函数作为径向基函数,支持向量作为径向基函数的中心构建RBF神经网络.运用改进的OBE(Optimal Bounding Ellipsoid)算法对RBF神经网络的权值进行辨识,得到与给定输入输出数据和噪声界序列一致的一类RBF神经网络.仿真算例验证了算法的有效性.

Based on support vector regression and radial basis function（RBF） neural network,the set-membership identification for nonlinear systems with unknown-but-bounded noise was investigated.The relationships among the ε-insensitive parameter,noise bounds and the number of support vectors were deduced,and the method of determining the ε-insensitive parameter using the noise bounds was introduced.The algorithm of choosing the scale of RBF neural network via support vector regression was described,in which the Gaussian kernel function was taken as the radial basis function and the support vector as its center parameters.After the structure of the RBF neural network was determined,all the feasible weight vectors of the RBF neural network were found by the optimal bounding ellipsoid（OBE） algorithm and a class of feasible nonlinear models were formed which were consistent with the given noise bound series and the input-output data set.A simulation example shows that the proposed algorithm is effective.