Title :
Any order approximate solution of the general langevin gradient state equation
Author :
Cao, Shao-zhong ; Dong, Jie ; Liu, He-ping ; Tu, Xu-Yan
Author_Institution :
Beijing Inst. of Graphic Commun., Beijing
Abstract :
To controlled systems under deterministic and random trade-off state, it is presented by general Langevin gradient equation while dynamic variational rule of the systems is described. The nonlinear differential equation is equivalent to its nonlinear Volterra´s integral equation of the second kind, and any order approximate solution of the equation is also obtained, by successive approximation method. Finally, the influence of random effect for system state is discussed.
Keywords :
Volterra equations; approximation theory; gradient methods; nonlinear differential equations; any order approximate solution; general Langevin gradient state equation; nonlinear Volterra integral equation; nonlinear differential equation; random effect; random trade-off state; successive approximation method; Approximation methods; Control systems; Differential equations; Information analysis; Integral equations; Nonlinear equations; Pattern analysis; Pattern recognition; State-space methods; Wavelet analysis; Random nonlinear system; Volterra’s integral equation; any order approximate solution; gradient equation;
Conference_Titel :
Wavelet Analysis and Pattern Recognition, 2007. ICWAPR '07. International Conference on
Conference_Location :
Beijing
Print_ISBN :
978-1-4244-1065-1
Electronic_ISBN :
978-1-4244-1066-8
DOI :
10.1109/ICWAPR.2007.4420634
