Numerical Solution of Some Types of Fractional Optimal Control Problems
We present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm “optimize first, then discretize”...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/306237 |
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| author | Nasser Hassan Sweilam Tamer Mostafa Al-Ajami Ronald H. W. Hoppe |
| author_facet | Nasser Hassan Sweilam Tamer Mostafa Al-Ajami Ronald H. W. Hoppe |
| author_sort | Nasser Hassan Sweilam |
| collection | DOAJ |
| description | We present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm “optimize first, then discretize” and relies on the approximation of the necessary optimality conditions in terms of the associated Hamiltonian. In the second approach, the state equation is discretized first using the Clenshaw and Curtis scheme for the numerical integration of nonsingular functions followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Two illustrative examples are included to demonstrate the validity and applicability of the suggested approaches. |
| format | Article |
| id | doaj-art-a24c07d04dbd4b78bc8021979c764691 |
| institution | OA Journals |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-a24c07d04dbd4b78bc8021979c7646912025-08-20T02:20:55ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/306237306237Numerical Solution of Some Types of Fractional Optimal Control ProblemsNasser Hassan Sweilam0Tamer Mostafa Al-Ajami1Ronald H. W. Hoppe2Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptInstitute of Mathematics, University of Augsburg, 86159 Augsburg, GermanyWe present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm “optimize first, then discretize” and relies on the approximation of the necessary optimality conditions in terms of the associated Hamiltonian. In the second approach, the state equation is discretized first using the Clenshaw and Curtis scheme for the numerical integration of nonsingular functions followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Two illustrative examples are included to demonstrate the validity and applicability of the suggested approaches.http://dx.doi.org/10.1155/2013/306237 |
| spellingShingle | Nasser Hassan Sweilam Tamer Mostafa Al-Ajami Ronald H. W. Hoppe Numerical Solution of Some Types of Fractional Optimal Control Problems The Scientific World Journal |
| title | Numerical Solution of Some Types of Fractional Optimal Control Problems |
| title_full | Numerical Solution of Some Types of Fractional Optimal Control Problems |
| title_fullStr | Numerical Solution of Some Types of Fractional Optimal Control Problems |
| title_full_unstemmed | Numerical Solution of Some Types of Fractional Optimal Control Problems |
| title_short | Numerical Solution of Some Types of Fractional Optimal Control Problems |
| title_sort | numerical solution of some types of fractional optimal control problems |
| url | http://dx.doi.org/10.1155/2013/306237 |
| work_keys_str_mv | AT nasserhassansweilam numericalsolutionofsometypesoffractionaloptimalcontrolproblems AT tamermostafaalajami numericalsolutionofsometypesoffractionaloptimalcontrolproblems AT ronaldhwhoppe numericalsolutionofsometypesoffractionaloptimalcontrolproblems |