A new efficient numerical scheme for solving fractional optimal control problems via a genocchi operational matrix of integration
In this paper, a new operational matrix of integration is derived using Genocchi polynomials, which is one of the Appell polynomials. By using the matrix, we develop an efficient, direct and new numerical method for solving a class of fractional optimal control problems. The fractional derivative in...
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SAGE Publications
2018
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| Online Access: | http://eprints.uthm.edu.my/3511/1/AJ%202018%20%28353%29.pdf http://eprints.uthm.edu.my/3511/ https://dx.doi.org/10.1177/1077546317698909 |
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| author | Phang, Chang Ismail, Noratiqah Farhana Isah, Abdulnasir Loh, Jian Rong |
| author_facet | Phang, Chang Ismail, Noratiqah Farhana Isah, Abdulnasir Loh, Jian Rong |
| author_sort | Phang, Chang |
| building | UTHM Library |
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| content_provider | Universiti Tun Hussein Onn Malaysia |
| content_source | UTHM Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | In this paper, a new operational matrix of integration is derived using Genocchi polynomials, which is one of the Appell polynomials. By using the matrix, we develop an efficient, direct and new numerical method for solving a class of fractional optimal control problems. The fractional derivative in the dynamic constraints was replaced with the Genocchi polynomials with unknown coefficients and a Genocchi operational matrix of fractional integration. Then, the equation derived from the dynamic constraints was put into the performance index. Hence, the fractional optimal control problems will be reduced to fractional variational problems. By finding a necessary condition for the optimality for the performance index, we will obtain a system of algebraic equations that can be easily solved by using any numerical method. Hence, we obtain the value of unknown coefficients of Genocchi polynomials. Lastly, the solution of the fractional optimal control problems will be obtained. In short, the properties of Genocchi polynomials are utilized to reduce the given problems to a system of algebraic equations. The approximation approach is simple to use and computer oriented. Illustrative examples are given to show the simplicity, accuracy and applicability of the method. |
| format | Article |
| id | my.uthm.eprints-3511 |
| institution | Universiti Tun Hussein Onn Malaysia |
| language | en |
| publishDate | 2018 |
| publisher | SAGE Publications |
| record_format | eprints |
| spelling | my.uthm.eprints-35112021-11-18T01:49:25Z http://eprints.uthm.edu.my/3511/ A new efficient numerical scheme for solving fractional optimal control problems via a genocchi operational matrix of integration Phang, Chang Ismail, Noratiqah Farhana Isah, Abdulnasir Loh, Jian Rong QA Mathematics In this paper, a new operational matrix of integration is derived using Genocchi polynomials, which is one of the Appell polynomials. By using the matrix, we develop an efficient, direct and new numerical method for solving a class of fractional optimal control problems. The fractional derivative in the dynamic constraints was replaced with the Genocchi polynomials with unknown coefficients and a Genocchi operational matrix of fractional integration. Then, the equation derived from the dynamic constraints was put into the performance index. Hence, the fractional optimal control problems will be reduced to fractional variational problems. By finding a necessary condition for the optimality for the performance index, we will obtain a system of algebraic equations that can be easily solved by using any numerical method. Hence, we obtain the value of unknown coefficients of Genocchi polynomials. Lastly, the solution of the fractional optimal control problems will be obtained. In short, the properties of Genocchi polynomials are utilized to reduce the given problems to a system of algebraic equations. The approximation approach is simple to use and computer oriented. Illustrative examples are given to show the simplicity, accuracy and applicability of the method. SAGE Publications 2018 Article PeerReviewed text en http://eprints.uthm.edu.my/3511/1/AJ%202018%20%28353%29.pdf Phang, Chang and Ismail, Noratiqah Farhana and Isah, Abdulnasir and Loh, Jian Rong (2018) A new efficient numerical scheme for solving fractional optimal control problems via a genocchi operational matrix of integration. Journal of Vibration and Control, Faculty of Science, Technology and Human Development,, 24 (14). pp. 3036-3048. ISSN 1077-5463 https://dx.doi.org/10.1177/1077546317698909 |
| spellingShingle | QA Mathematics Phang, Chang Ismail, Noratiqah Farhana Isah, Abdulnasir Loh, Jian Rong A new efficient numerical scheme for solving fractional optimal control problems via a genocchi operational matrix of integration |
| title | A new efficient numerical scheme for solving fractional optimal control problems via a genocchi operational matrix of integration |
| title_full | A new efficient numerical scheme for solving fractional optimal control problems via a genocchi operational matrix of integration |
| title_fullStr | A new efficient numerical scheme for solving fractional optimal control problems via a genocchi operational matrix of integration |
| title_full_unstemmed | A new efficient numerical scheme for solving fractional optimal control problems via a genocchi operational matrix of integration |
| title_short | A new efficient numerical scheme for solving fractional optimal control problems via a genocchi operational matrix of integration |
| title_sort | new efficient numerical scheme for solving fractional optimal control problems via a genocchi operational matrix of integration |
| topic | QA Mathematics |
| url | http://eprints.uthm.edu.my/3511/1/AJ%202018%20%28353%29.pdf http://eprints.uthm.edu.my/3511/ https://dx.doi.org/10.1177/1077546317698909 |
| url_provider | http://eprints.uthm.edu.my/ |