$L^p(K)$中RBF神经网络的系统识别问题

$L^p(K)$ Approximation Problems in System Identification with RBF Neural Networks

中文关键词:  RBF神经网络  系统识别  $L^p$逼近  连续泛函和算子.

英文关键词:RBF neural networks  system identification  $L^p$-approximation  continuous functionals and operators.

中文摘要:

      本文主要研究RBF神经网络在系统识别上的$L^p$逼近问题.文中证明了用$L^p_{loc}$中一元非多项式函数的复合,可以逼近定义在$L^p(K)$上的连续泛函,以及$L^{p_1}(K_1)$到$L^{p_2}(K_2)$的连续算子. 这个结果表明,若RBF神经网络的激活函数选为$L^p_{loc}$中的任意非偶次多项式函数,则该神经网络就能以任意精度识别上述系统.

英文摘要:

      $L^p$ approximation problems in system identification with RBF neural networks are investigated. It is proved that by superpositions of some functions of one variable in $L^p_{\rm loc}({\mathbb R})$, one can approximate continuous functionals defined on a compact subset of $L^p(K)$ and continuous operators from a compact subset of $L^{p_1}(K_1)$ to a compact subset of $L^{p_2}(K_2)$. These results show that if its activation function is in $L^p_{\rm loc}({\mathbb R})$ and is not an even polynomial, then this RBF neural networks can approximate the above systems with any accuracy.