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.
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,the linear solution of the state equation is given.Then,by use of the trial and error method,substituting the trial and error solution with series expression into two sides of the state equation for general affine nonlinear systems,any order approximate solution with series expression is obtained by comparing coefficients of the same items of two sides for these equations.
出处
《东南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2009年第S1期43-47,共5页
Journal of Southeast University：Natural Science Edition
基金
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
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
general affine nonlinear system
state equation
any order approximate series solution
trial and error method
