Arbitrary-Order Approximate Solution to Integral State Equation for Generalized Atone Nonlinear Systems  

作　　者：CAO Shaozhong LI Yang TU Xuyan 

机构地区：[1]School of Information and Mechanical Engineering, Beijing Institute of Graphic Communication, Beijing 102600, China [2]School of Information Engineering, University of Science and Technology Beijing, Beijing 100083, China

出　　处：《Chinese Journal of Electronics》2010年第3期441-445,共5页电子学报（英文版）

基　　金：This work is supported by Beijing Natural Science Foundation （No.4092013）, Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality （No.TXM2007_014223_044661）, Funding Project for Science and Technology Research of Beijing Municipal Commission of Education （No.KM200810015003）, Funding Project for Science and Technology Research on the Talents Introduced into Beijing Institute of Graphic Communication （No.09170107019）, Major Project for Science and Technology of Beijing Institute of Graphic Communication.

摘　　要：Compared with affine system, the generalized affine system is one more universal nonlinear control system, in which both state variables and control variables are nonlinear. In this paper, from the differential equation of generalized affine nonlinear system, the solution of its homogeneous equation is obtained. The differential equation is converted to the fully equivalent integral equation by the method of variation of parameters. Therefore, the recursion formula of the approximate solution to integral equation is given by heuristic method. And then based on the recursion formula, the arbitrary-order approximate series solution to integral equation is obtained. And the theory of integral equation is employed to prove the convergence.

关 键 词：Generalized affine nonlinear system State equation Series solution. 

分 类 号：O226[理学—运筹学与控制论] TP271[理学—数学]