Using shifted Legendre orthonormal polynomials for solving fractional optimal control problems

Document Type : Research Article

Authors

• R. Naseri ¹
• A. Heydari ¹
• A.S. Bagherzadeh ²

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

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

10.22067/ijnao.2022.70466.1035

Abstract

‎‎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.

Keywords

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

Main Subjects

• Optimal Control

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