Using shifted Legendre orthonormal polynomials for solving fractional optimal control problems

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 18 اسفند 1400  

نوع مقاله: SPECIAL ISSUE- Volume 12 No 2 (Summer 2022)

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.70466.1035

نویسندگان

Roghayeh Naseri ¹؛ Aghileh Heydari ¹؛ Amir Saboor Bagheradeh ²

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

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

چکیده

‎In this paper‎, ‎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