Using shifted Legendre orthonormal polynomials for solving fractional optimal control problems

Iranian Journal of Numerical Analysis and Optimization

مقاله 2، دوره 12، Issue 3 (Special Issue) - شماره پیاپی 23، بهمن 2022، صفحه 513-532   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.70466.1035

نویسندگان

R. Naseri^{* 1}؛ A. Heydari¹؛ A.S. Bagherzadeh²

¹Department of Mathematics, Payame Noor University (PNU), P.O.Box 19395-4697, Tehran, Iran.

²Department of Applied Mathematics, Faculty of Mathematical Science, Ferdowsi University of Mashhad, Mashhad, Iran.

چکیده

‎‎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.

کلیدواژه‌ها

Fractional optimal control problem (FOCP)؛ Shifted Legendre orthonormal polynomials (SLOPs)؛ Caputo fractional derivative

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