Design and performance analysis of deterministic learning of sampled-data nonlinear systems  

作　　者：YUAN ChengZhi WANG Cong 

机构地区：[1]College of Automation and the Center for Control and Optimization,South China University of Technology

出　　处：《Science China(Information Sciences)》2014年第3期199-216,共18页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Fund for Distinguished Young Scholars(Grant No.61225014);National Natural Science Foundation of China(Grant No.60934001)

摘　　要：In this paper, we extend the deterministic learning theory to sampled-data nonlinear systems. Based on the Euler approximate model, the adaptive neural network identifier with a normalized learning algorithm is proposed. It is proven that by properly setting the sampling period, the overall system can be guaranteed to be stable and partial neural network weights can exponentially converge to their optimal values under the satisfaction of the partial persistent excitation （PE） condition. Consequently, locally accurate learning of the nonlinear dynamics can be achieved, and the knowledge can be represented by using constant-weight neural networks. Furthermore, we present a performance analysis for the learning algorithm by developing explicit bounds on the learning rate and accuracy. Several factors that influence learning, including the PE level, the learning gain, and the sampling period, are investigated. Simulation studies are included to demonstrate the effectiveness of the approach.In this paper, we extend the deterministic learning theory to sampled-data nonlinear systems. Based on the Euler approximate model, the adaptive neural network identifier with a normalized learning algorithm is proposed. It is proven that by properly setting the sampling period, the overall system can be guaranteed to be stable and partial neural network weights can exponentially converge to their optimal values under the satisfaction of the partial persistent excitation （PE） condition. Consequently, locally accurate learning of the nonlinear dynamics can be achieved, and the knowledge can be represented by using constant-weight neural networks. Furthermore, we present a performance analysis for the learning algorithm by developing explicit bounds on the learning rate and accuracy. Several factors that influence learning, including the PE level, the learning gain, and the sampling period, are investigated. Simulation studies are included to demonstrate the effectiveness of the approach.

关 键 词：neural network identification deterministic learning persistent excitation sampled-data systems radial basis function networks （RBFNs） 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]