Any Order Approximate Solution of the State Equation for Uncontrolled Random Nonlinear Systems
Xuyan Tu · Dianzi xuebao · 2008
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.