Volterra series approximation for rational nonlinear system

被引：0
作者：
Wang Q. [1 ]
Xu P. [2 ]
Wong N. [1 ]
机构：
[1] Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong, Pokfulam Road
[2] Academy of Mathematics and System Sciences, Chinese Academy of Sciences
来源：
Journal of Applied Mathematics and Computing | 2014年 / 45卷 / 1-2期
关键词：
Approximate solution; Nonlinear system; Singular system; Volterra series;
D O I：
10.1007/s12190-013-0729-2
中图分类号：
学科分类号：
摘要：
Rational nonlinear systems are widely used to model the phenomena in mechanics, biology, physics and engineering. However, there are no exact analytical solutions for rational nonlinear system. Hence, the approximate analytical solutions are good choices as they can give the estimation of the states for system analysis, controller design and reduction. In this paper, an approximate analytical solution for rational nonlinear system is derived in terms of the solution of a polynomial system by Volterra series theory. The rational nonlinear system is transformed to a singular polynomial system with finite terms by adding some algebraic constraints related to the rational terms. The analytical solution of singular polynomial system is approximated by the summation of the solutions of Volterra singular subsystems. Their analytical solutions are derived by a novel regularization algorithm. The first fourth Volterra subsystems are enough to approximate the analytical solution to guarantee the accuracy. Results of numerical experiments are reported to show the effectiveness of the proposed method. © 2013 Korean Society for Computational and Applied Mathematics.
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页码：411 / 432
页数：21
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