非线性受控系统状态方程的任意阶近似解  

Any order approximate solution of state equation for nonlinear controlled systems

作　　者：曹少中[1] 刘贺平[1] 涂序彦[1] 

机构地区：[1]北京科技大学信息工程学院

出　　处：《控制与决策》2008年第4期378-381,共4页Control and Decision

基　　金：国家自然科学基金项目(60375038,60374032,60673101);国家863计划项目(2006AA04Z110)

摘　　要：针对工作在理想状态附近的受控系统,通过对其非线性状态方程进行Taylor展开,使之变为无穷级数形式的常微分方程组;然后在线性状态方程组解的基础上采用常数变异法,使之变换成积分方程;最后采用逐次逼近法求得非线性状态方程的任意阶近似解,并进一步讨论了系统状态的方均包络矩阵的转移规律.By making of the Taylor expansion, the nonlinear state equation of controlled systems under ideal state is converted to a set of ordinary differential equations with infinite series expression. Based on the solution of linear state equation system, the integral equation of the nonlinear state equation is obtained by using constant variation method; Finally, any order approximate solution of the nonlinear state equation is given by using successive approximation method, and the transfer rules of mean square envelope matrix for the state of nonlinear systems is also discussed.

关 键 词：TAYLOR展开 包络矩阵 VOLTERRA积分方程 任意阶近似解 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]