Any order approximate solution of the state equation for an affine nonlinear system

CAO Shaozhong; LIU Heping; TU Xuyan

doi:10.13374/j.issn1001-053x.2008.06.023

Volume 30 Issue 6

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CAO Shaozhong, LIU Heping, TU Xuyan. Any order approximate solution of the state equation for an affine nonlinear system[J]. Chinese Journal of Engineering, 2008, 30(6): 690-693. doi: 10.13374/j.issn1001-053x.2008.06.023

Citation:

CAO Shaozhong, LIU Heping, TU Xuyan. Any order approximate solution of the state equation for an affine nonlinear system[J]. Chinese Journal of Engineering, 2008, 30(6): 690-693. doi: 10.13374/j.issn1001-053x.2008.06.023

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Any order approximate solution of the state equation for an affine nonlinear system

doi: 10.13374/j.issn1001-053x.2008.06.023

1. College of Information & Mechanical Engineering, Beijing Institute of Graphic Communication, Beijing 102600, China;
2. School of Information Engineering, University of Science and Technology Beijing, Beijing 100083, China

Received Date: 2007-04-12
Rev Recd Date: 2007-07-25

Available Online: 2021-08-06

Abstract

Abstract

The state equation of an typical affine nonlinear system was solved with the ordinary differential equation theory. By utilizing the expansion expression of equilibrium point of the system, the homogeneous equation's solution was obtained, and then the nonlinear differential equation was equivalent to its nonlinear Volterra's integral equation of the second kind by the constant variation method. Any order approximate solution of the equation was presented, and its convergence was mathematically proved by the successive approximation method.
- nonlinear system,
- state equation,
- ordinary differential equation,
- Volterra's integral equation,
- successive approximation method,
- approximate solution