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Solution of linear optimal control problems with time delay using a composite Chebyshev finite difference method
Author(s) -
Marzban H.R.,
Hoseini S.M.
Publication year - 2012
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/oca.2019
Subject(s) - chebyshev filter , chebyshev iteration , mathematics , chebyshev equation , chebyshev polynomials , chebyshev nodes , finite difference , finite difference method , mathematical analysis , orthogonal polynomials , classical orthogonal polynomials
SUMMARY In this paper, a composite Chebyshev finite difference method is introduced and applied for finding the solution of optimal control of time‐delay systems with a quadratic performance index. This method is an extension of the Chebyshev finite difference scheme. The proposed method can be regarded as a nonuniform finite difference scheme and is based on a hybrid of block‐pulse functions and Chebyshev polynomials using the well‐known Chebyshev–Gauss–Lobatto points. Various types of time‐delay systems are included to demonstrate the validity and the applicability of the technique. The method is easy to implement and provides very accurate results. Copyright © 2012 John Wiley & Sons, Ltd.