2005
DOI: 10.1080/00207160512331323407
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Numerically efficient approximations to the optimal control of linear singularly perturbed systems based on Haar wavelets

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Cited by 41 publications
(11 citation statements)
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“…However, this approach is nonrecursive in nature. Haar wavelet approach [9] has been presented to study the optimal control problem of linear singularly perturbed systems. In the recent times, Fourier series [10], Chebyshev polynomials of first kind [11] and Legendre wavelets [12] have been applied for solving optimal control problem of singular systems.…”
Section: Introductionmentioning
confidence: 99%
“…However, this approach is nonrecursive in nature. Haar wavelet approach [9] has been presented to study the optimal control problem of linear singularly perturbed systems. In the recent times, Fourier series [10], Chebyshev polynomials of first kind [11] and Legendre wavelets [12] have been applied for solving optimal control problem of singular systems.…”
Section: Introductionmentioning
confidence: 99%
“…For example, Karimi and Lohmann [ 17 ] applied the Haar functions for modeling and robust control of bounce and pitch vibration for the enginebody vibration structure. Also, the Haar wavelet method has been investigated for optimal control of time-varying state-delayed [ 18 ], linear singularly perturbed systems [ 19 ], and second-order linear systems [ 20 ]. In addition, based on the properties of orthogonal Sinc functions, it is apparent that the convergence rate of approximation is exponential [ 21 ].…”
Section: Introductionmentioning
confidence: 99%
“…It is proved that wavelets are powerful tools for exploring new problems and solving differential equations. The Haar wavelets are alternative tools that have been studied for similar purposes; see [16][17][18][19].…”
Section: Introductionmentioning
confidence: 99%