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Numerical solution a class of 2D fractional optimal control problems by using 2D Müntz‐Legendre wavelets
Author(s) -
Rahimkhani Parisa,
Ordokhani Yadollah
Publication year - 2018
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.2456
Subject(s) - legendre wavelet , legendre polynomials , wavelet , fractional calculus , mathematics , class (philosophy) , order (exchange) , matrix (chemical analysis) , legendre function , mathematical optimization , mathematical analysis , computer science , wavelet transform , discrete wavelet transform , materials science , finance , artificial intelligence , economics , composite material
Summary In this paper, a method for finding an approximate solution of a class of 2D fractional optimal control problems with fractional‐order dynamical system is discussed. In the proposed method, the fractional derivative is expressed in the Caputo sense. The method consists of expanding unknown functions as the elements of two‐dimensional (2D) Müntz‐Legendre wavelets. The 2D Müntz‐Legendre wavelets are constructed and their properties are presented. The operational matrix of fractional‐order integration for these wavelets is utilized to reduce the solution of 2D fractional optimal control problem to an optimization problem, which can then be solved easily. Some results concerning the error analysis are obtained. Finally, two illustrative test problems are included to demonstrate the validity and applicability of the technique. Moreover, our achievements are compared with the previous results to show the superiority of the proposed method.