Title :
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
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;
Conference_Titel :
Digital Signal Processing Workshop Proceedings, 1996., IEEE
Conference_Location :
Loen
Print_ISBN :
0-7803-3629-1
DOI :
10.1109/DSPWS.1996.555548
