随机非线性系统自由状态方程的任意阶近似解  

Any Order Approximate Solution of the State Equation for Uncontrolled Random Nonlinear Systems

作　　者：曹少中[1] 刘贺平[2] 涂序彦[2] 

机构地区：[1]北京印刷学院信息与机电工程学院,北京102600 [2]北京科技大学信息工程学院,北京100083

出　　处：《电子学报》2008年第4期785-788,共4页Acta Electronica Sinica

基　　金：国家自然科学基金(No.60673101,No.60374032);国家863高技术研究发展计划(No.2006AA04Z110);北京市中青年骨干教师培养计划,北京印刷学院引进人才项目;北京市教育委员会科技发展计划面上项目(No.KM200810015003)

摘　　要：针对非线性系统的随机性的特点,提出了随机非线性系统自由状态方程的任意阶近似解法.该解法从自由状态空间中的广义朗之万梯度方程出发,利用常数变易法导出了与广义朗之万方程等价的广义的第二类非线性、随机性Valterra积分方程,采用逐次逼近法求得了方程的任意阶近似解.最后,讨论了非线性、随机性对系统状态空间转移的影响.随机非线性系统自由状态方程的任意阶近似解法为随机非线性系统的定量分析提供了一种有效方法.Armed at the difficult solution of uncontrolled random nonlinear systems,a method for any order approximate solution of the state equation for uncontrolled random nonlinear systems is proposed. Based on general Langevin gradient equation in uncontrolled state space, the random nonlinear Volterra＇s integral equation for the second kind, which is equivalent to general Langevin gradient equation, is obtained, by utilizing constant variation method. Then, any order approximate solution of the equation is also obtained, by successive approximation method. Finally, the influences of nonlinearity and randomness for state space transformation of the system is discussed. The method for any order approximate solution of the state equation for uncontrolled random nonlinear systems is an effective method of quantitative analysis for random nonlinear systems.

关 键 词：随机非线性系统 朗之万梯度方程 Vaherra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]