仿射非線性系統狀態方程的任意階近似解

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仿射非線性系統狀態方程的任意階近似解

曹少中, 劉賀平, 涂序彥

文章導航 > 工程科學學報 > 2008 > 30(6): 690-693

曹少中, 劉賀平, 涂序彥. 仿射非線性系統狀態方程的任意階近似解[J]. 工程科學學報, 2008, 30(6): 690-693. doi: 10.13374/j.issn1001-053x.2008.06.023

引用本文:

曹少中, 劉賀平, 涂序彥. 仿射非線性系統狀態方程的任意階近似解[J]. 工程科學學報, 2008, 30(6): 690-693. doi: 10.13374/j.issn1001-053x.2008.06.023

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

曹少中, 劉賀平, 涂序彥. 仿射非線性系統狀態方程的任意階近似解[J]. 工程科學學報, 2008, 30(6): 690-693. doi: 10.13374/j.issn1001-053x.2008.06.023

引用本文:

曹少中, 劉賀平, 涂序彥. 仿射非線性系統狀態方程的任意階近似解[J]. 工程科學學報, 2008, 30(6): 690-693. doi: 10.13374/j.issn1001-053x.2008.06.023

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

仿射非線性系統狀態方程的任意階近似解

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

1. 北京印刷學院信息與機電工程學院, 北京 102600;
2. 北京科技大學信息工程學院, 北京 100083

基金項目:

北京市教育委員會科技發展計劃面上項目(No.KM200810015003)

北京印刷學院引進人才科技研究項目(No.09170107019)

國家自然科學基金資助項目(No.60374032,No.60673101)

北京市屬市管高等學校人才強教計劃資助項目(No.TXM2007-014223-044661)

作者簡介:
曹少中(1965-),男,副教授,博士,E-mail:cszh6502@163.com

中圖分類號: TP273
計量
- 文章訪問數: 140
- HTML全文瀏覽量: 31
- PDF下載量: 4
- 被引次數: 0
出版歷程
- 收稿日期: 2007-04-12
- 修回日期: 2007-07-25
- 網絡出版日期: 2021-08-06

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

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

摘要: 針對典型的仿射非線性系統,采用常微分方程理論對其進行求解.首先將系統在平衡點附近進行展開,求得其齊次方程的解,然后利用常數變易法將非線性微分方程變為等價的第二類非線性Volterra積分方程.采用逐次逼近法,求得任意階近似解,并證明解的收斂性.
- 非線性系統 /
- 狀態方程 /
- 常微分方程 /
- VOLTERRA積分方程 /
- 逐次逼近法 /
- 近似解
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

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文章訪問數: 140
HTML全文瀏覽量: 31
PDF下載量: 4
被引次數: 0

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