Wavelets in dynamics, optimal control and Galerkin approximations

Author

Fedorova, A.N. ; Zeitlin, M.G.

Author_Institution

Inst. of Problems of Mech. Eng., Acad. of Sci., St. Petersburg, Russia

fYear

1996

Firstpage

409

Lastpage

412

Abstract

We give the explicit time description of the following nonlinear (polynomial) problems: dynamics and optimal dynamics for some important electromechanical system, Galerkin approximation for beam equation, and detecting chaos in the Melnikov approach. We present the solution in a compactly supported wavelet basis. The solution is parameterized by solutions of two reduced algebraical problems, the first is nonlinear (polynomial), the second is a linear problem, which is obtained from one of the next wavelet construction: fast wavelet transform, stationary subdivision schemes, the method of connection coefficients

Keywords

Galerkin method; approximation theory; chaos; dynamics; optimal control; partial differential equations; polynomials; signal detection; signal resolution; wavelet transforms; Galerkin approximation; Galerkin approximations; Melnikov approach; beam equation; chaos detection; compactly supported wavelet basis; connection coefficients method; dynamics; electromechanical system; explicit time description; fast wavelet transform; linear problem; multiresolution expansion; nonlinear polynomial problems; optimal control; optimal dynamics; partial differential equations; reduced algebraical problems; signal detection; stationary subdivision; wavelet construction; Electromechanical systems; Mathematical model; Mechanical engineering; Milling machines; Nonlinear dynamical systems; Nonlinear equations; Optimal control; Polynomials; Riccati equations; Wavelet transforms;

fLanguage

English

Publisher

ieee

Conference_Titel

Digital Signal Processing Workshop Proceedings, 1996., IEEE

Conference_Location

Loen

Print_ISBN

0-7803-3629-1

Type

conf

DOI

10.1109/DSPWS.1996.555548

Filename

555548