Using shifted Legendre orthonormal polynomials for solving fractional optimal control problems
| Autor: | R. Naseri, A. Heydari, A.S. Bagherzadeh |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Iranian Journal of Numerical Analysis and Optimization, Vol 12, Iss Issue 3 (Special Issue), Pp 513-532 (2022) |
| Druh dokumentu: | article |
| ISSN: | 2423-6977 2423-6969 |
| DOI: | 10.22067/ijnao.2022.70466.1035 |
| Popis: | shifted Legendre orthonormal polynomials (SLOPs) are used to approximate the numerical solutions of fractional optimal control problems. To do so, first, the operational matrix of the Caputo fractional derivative, the SLOPs, and Lagrange multipliers are used to convert such problems into algebraic equations. Also, the method is proposed for solving multidimensional problems. We obtained the error bound of the operational matrix in fractional derivatives and proved the convergence of the method. Then, this is tested on some nonlinear examples. Comparison of our results with those obtained by other techniques in previous studies revealed the accuracy of the proposed technique for nonlinear and multidimensional problems. |
| Databáze: | Directory of Open Access Journals |
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