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

Volume

1

fYear

2007

fDate

2-4 Nov. 2007

Firstpage

49

Lastpage

52

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;

fLanguage

English

Publisher

ieee

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

Type

conf

DOI

10.1109/ICWAPR.2007.4420634

Filename

4420634