Spectral tau algorithm for solving a class of fractional optimal control problems via Jacobi polynomials
This paper is dedicated to analyzing and presenting an efficient numerical algorithm for solving a class of fractional optimal control problems (FOCPs). The basic idea behind the suggested algorithm is based on transforming the FOCP under investigation into a coupled system of fractional-order diffe...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Balikesir University
2018-04-01
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| Series: | An International Journal of Optimization and Control: Theories & Applications |
| Subjects: | |
| Online Access: | http://ijocta.org/index.php/files/article/view/442 |
| _version_ | 1797907115605491712 |
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| author | Youssri H. Youssri Waleed M. Abd-Elhameed |
| author_facet | Youssri H. Youssri Waleed M. Abd-Elhameed |
| author_sort | Youssri H. Youssri |
| collection | DOAJ |
| description | This paper is dedicated to analyzing and presenting an efficient numerical algorithm for solving a class of fractional optimal control problems (FOCPs). The basic idea behind the suggested algorithm is based on transforming the FOCP under investigation into a coupled system of fractional-order differential equations whose solutions can be expanded in terms of the Jacobi basis. With the aid of the spectral-tau method, the problem can be reduced into a system of algebraic equations which can be solved via any suitable solver. Some illustrative examples and comparisons are presented aiming to demonstrate the accuracy, applicability, and efficiency of the proposed algorithm. |
| first_indexed | 2024-04-10T10:31:24Z |
| format | Article |
| id | doaj.art-d0f2df0388ee46dfae5de34bffb8bb95 |
| institution | Directory Open Access Journal |
| issn | 2146-0957 2146-5703 |
| language | English |
| last_indexed | 2024-04-10T10:31:24Z |
| publishDate | 2018-04-01 |
| publisher | Balikesir University |
| record_format | Article |
| series | An International Journal of Optimization and Control: Theories & Applications |
| spelling | doaj.art-d0f2df0388ee46dfae5de34bffb8bb952023-02-15T16:21:06ZengBalikesir UniversityAn International Journal of Optimization and Control: Theories & Applications2146-09572146-57032018-04-018210.11121/ijocta.01.2018.00442Spectral tau algorithm for solving a class of fractional optimal control problems via Jacobi polynomialsYoussri H. Youssri0Waleed M. Abd-Elhameed1Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptThis paper is dedicated to analyzing and presenting an efficient numerical algorithm for solving a class of fractional optimal control problems (FOCPs). The basic idea behind the suggested algorithm is based on transforming the FOCP under investigation into a coupled system of fractional-order differential equations whose solutions can be expanded in terms of the Jacobi basis. With the aid of the spectral-tau method, the problem can be reduced into a system of algebraic equations which can be solved via any suitable solver. Some illustrative examples and comparisons are presented aiming to demonstrate the accuracy, applicability, and efficiency of the proposed algorithm.http://ijocta.org/index.php/files/article/view/442Jacobi polynomialstau methodNewton's iterative methodoptimal control problemssystem of fractional differential equations |
| spellingShingle | Youssri H. Youssri Waleed M. Abd-Elhameed Spectral tau algorithm for solving a class of fractional optimal control problems via Jacobi polynomials An International Journal of Optimization and Control: Theories & Applications Jacobi polynomials tau method Newton's iterative method optimal control problems system of fractional differential equations |
| title | Spectral tau algorithm for solving a class of fractional optimal control problems via Jacobi polynomials |
| title_full | Spectral tau algorithm for solving a class of fractional optimal control problems via Jacobi polynomials |
| title_fullStr | Spectral tau algorithm for solving a class of fractional optimal control problems via Jacobi polynomials |
| title_full_unstemmed | Spectral tau algorithm for solving a class of fractional optimal control problems via Jacobi polynomials |
| title_short | Spectral tau algorithm for solving a class of fractional optimal control problems via Jacobi polynomials |
| title_sort | spectral tau algorithm for solving a class of fractional optimal control problems via jacobi polynomials |
| topic | Jacobi polynomials tau method Newton's iterative method optimal control problems system of fractional differential equations |
| url | http://ijocta.org/index.php/files/article/view/442 |
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