Deterministic learning of completely resonant nonlinear wave systems with Dirichlet boundary conditions

作     者：Tao Peng Cong Wang 

作者机构：College of Automation Science and Engineering South China University of Technology Guangzhou Guangdong 510640 China 

出 版 物：《控制理论与应用（英文版）》 (J. Control Theory Appl.)

年 卷 期：2012年第10卷第2期

页      面：201-209页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 081104[工学-模式识别与智能系统] 08[工学] 070104[理学-应用数学] 0701[理学-数学] 0811[工学-控制科学与工程] 071102[理学-系统分析与集成] 081103[工学-系统工程] 

基　　金：supported by the National Natural Science Foundation of China (Nos. 60934001, 90816028) the Fundamental Research Funds for the Central Universities, South China University of Technology 

主　　题：Deterministic learning Wave system Completely resonant Finite-dimensional approximation RBF neu-ral networks System dynamics 

摘      要：In this paper, we investigate the approximation of completely resonant nonlinear wave systems via deter- ministic learning. The plants are distributed parameter systems （DPS） describing homogeneous and isotropic elastic vibrat- ing strings with fixed endpoints. The purpose of the paper is to approximate the infinite-dimensional dynamics, rather than the parameters of the wave systems. To solve the problem, the wave systems are first transformed into finite-dimensional dynamical systems described by ordinary differential equation （ODE）. The properties of the finite-dimensional systems, including the convergence of the solution, as well as the dominance of partial system dynamics according to point-wise measurements, are analyzed. Based on the properties, second, by using the deterministic learning algorithm, an approxi- mately accurate neural network （NN） approximation of the the finite-dimensional system dynamics is achieved in a local region along the recurrent trajectories. Simulation studies are included to demonstrate the effectiveness of the proposed approach.