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Pseudospectral method for fractional infinite horizon optimal control problems
Author(s) -
Yang Yin,
Noori Skandari M. H.
Publication year - 2020
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.2649
Subject(s) - pseudospectral optimal control , fractional calculus , optimal control , mathematics , chebyshev pseudospectral method , domain (mathematical analysis) , nonlinear system , transformation (genetics) , gauss pseudospectral method , horizon , mathematical optimization , mathematical analysis , pseudo spectral method , fourier transform , geometry , classical orthogonal polynomials , fourier analysis , chebyshev equation , orthogonal polynomials , biochemistry , physics , chemistry , quantum mechanics , gene
Summary Up to now, several numerical methods have been presented to solve finite horizon fractional optimal control problems by researchers, while solving fractional optimal control problems on infinite domain is a challenging work. Hence, in this article, a numerical method is proposed to solve fractional infinite horizon optimal control problems. At the first stage, a domain transformation technique is used to map the infinite domain to a finite horizon. Also, fractional derivative defined on an unbounded domain is converted into an equivalent derivative on a finite domain. Then, a new shifted Legendre pseudospectral method is utilized to solve the obtained finite problem and a nonlinear programming problem is suggested to approximate the optimal solutions. Finally, some numerical examples are given to show the efficiency of the method.