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State analysis and optimal control of linear time‐varying systems via Haar wavelets
Author(s) -
Hsiao ChunHui,
Wang WenJune
Publication year - 1998
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/(sici)1099-1514(199811/12)19:6<423::aid-oca638>3.0.co;2-g
Subject(s) - haar , wavelet , haar wavelet , mathematics , matrix (chemical analysis) , coefficient matrix , orthogonal matrix , orthogonal functions , adjoint equation , discrete wavelet transform , mathematical optimization , computer science , wavelet transform , mathematical analysis , eigenvalues and eigenvectors , partial differential equation , orthogonal basis , artificial intelligence , materials science , physics , quantum mechanics , composite material
State analysis and optimization of time‐varying systems via Haar wavelets are proposed in this paper. Based upon some useful properties of Haar functions, a special product matrix and a related coefficient matrix are applied to solve the time‐varying systems first. Then the backward integration is introduced to solve the adjoint equation of optimization. The unknown Haar coefficient matrix will be in generalized Lyapunov equation form, which is solved via a single‐term algorithm. The local property of Haar wavelets is fully applied to shorten the calculation process. A brief comparison between Haar wavelet and other orthogonal functions is also given. Copyright © 1998 John Wiley & Sons, Ltd.