The pseudo-linearization and any order approximate analytical solutions for nonlinear dynamical equation

Author

Cao, Shaozhong ; Li, Yang

Author_Institution

Sch. of Inf. & Mech. Eng., Beijing Inst. of Graphic Commun., Beijing, China

fYear

2012

Firstpage

54

Lastpage

58

Abstract

The integrand is expanded as the Taylor series, at the initial state of time-state space, by introducing the concept of time-state space and the method of pseudo-linearization. The any order approximate general analytical solutions are obtained by directed integrating, and proven to be convergent. Compared with the general method of linear or nonlinear removal, this method can simplify the calculation for non-commutative system and commutative time-varying system. The method is also proven to be universal.

Keywords

approximation theory; nonlinear equations; series (mathematics); time-varying systems; Taylor series; approximate general analytical solution; commutative time-varying system; integrand; linear removal; noncommutative calculation system; nonlinear dynamical equation; nonlinear removal; pseudolinearization method; time-state space; Approximation methods; Differential equations; Equations; Mathematical model; Nonlinear dynamical systems; Taylor series; Vectors; analytical solution; nonlinear dynamical equation; pseudo-linearization;

fLanguage

English

Publisher

ieee

Conference_Titel

Intelligent Control, Automatic Detection and High-End Equipment (ICADE), 2012 IEEE International Conference on

Conference_Location

Beijing

Print_ISBN

978-1-4673-1331-5

Type

conf

DOI

10.1109/ICADE.2012.6330098

Filename

6330098