| 广义仿射非线性系统状态方程的任意阶近似级数解 |
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| 引用本文： | 曹少中,李旸,涂序彦. 广义仿射非线性系统状态方程的任意阶近似级数解[J]. 东南大学学报(自然科学版), 2009, 0(Z1) |
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| 作者姓名： | 曹少中 李旸 涂序彦 |
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| 作者单位： | 北京印刷学院信息与机电工程学院;北京科技大学信息工程学院; |
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| 基金项目： | 北京市自然科学基金资助项目(4092013); 北京市属高等学校人才强教计划资助项目; 北京市教委科技面上项目(KM200810015003); 北京印刷学院引进人才资助项目(09170107019); 北京印刷学院科技重点资助项目 |
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| 摘 要： | 为了分析广义仿射非线性系统,对于广义仿射非线性系统状态方程,应用Taylor级数理论,将方程右端先后对控制量及状态量作Taylor展开,使之变为状态量的无穷级数形式,而控制量只出现在状态量各次项的系数中,方程的右端分为状态量的线性项和非线性高次项2部分.为了求解广义仿射非线性系统状态方程,首先应用Picard递归积分法求得对应齐次状态方程的线性解.然后采用试探法,将级数形式的试探解代入广义仿射非线性系统状态方程两端,通过比较系数,求得方程的任意阶近似级数解析解.
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| 关 键 词： | 广义仿射非线性系统 状态方程 任意阶近似级数解 试探法 |
Any order approximate series solution of the state equation for general affine nonlinear systems |
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| Cao Shaozhong Li Yang Tu Xuyan. Any order approximate series solution of the state equation for general affine nonlinear systems[J]. Journal of Southeast University(Natural Science Edition), 2009, 0(Z1) |
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| Authors: | Cao Shaozhong Li Yang Tu Xuyan |
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| Affiliation: | Cao Shaozhong1 Li Yang1 Tu Xuyan2(1 College of Information , Mechanical Engineering,Beijing Institute of Graphic Communication,Beijing 102600,China)(2 School of Information Engineering,University of Science , Technology Beijing,Beijing 100083,China) |
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| Abstract: | In order to analyze general affine nonlinear systems,according to the theory of Taylor series,the state equations are converted to a set of equations for state variation with infinite series expression using the Taylor expansion on control variations and state variations,while the control variations are included in the coefficient of state variations.The right side of this equation includes linear items and nonlinear items.In order to solve these equations,utilizing the Picard recurrence integrating method,... |
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| Keywords: | general affine nonlinear system state equation any order approximate series solution trial and error method |
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