A Numerical Method to Solve Fuzzy Fractional Optimal Control Problems Using Legendre Basis Functions

M. Mirvakili (), T. Allahviranloo and F. Soltanian ()
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M. Mirvakili: Department of Mathematics, Payame Noor University, P.O. Box 19395–3697, Tehran, Iran
T. Allahviranloo: #x2020;Bahcesehir University, Faculty of Engineering and Natural Science, Istanbul, Turkey
F. Soltanian: Department of Mathematics, Payame Noor University, P.O. Box 19395–3697, Tehran, Iran

New Mathematics and Natural Computation (NMNC), 2021, vol. 17, issue 01, 63-90

Abstract: In this paper, a solution scheme for a class of Fuzzy Fractional Optimal Control Problems (FFOCPs) in Caputo sense is presented using the Legendre basis functions. The control variable will be found so that it minimizes a quadratic performance function. Having the Euler–Lagrange equations for FFOCP and using the distance function, the problem is divided into a couple of parts which are solved in a system of equations and the approximate numerical solution of the equations is obtained. Through two examples, one time invariant and the other time varying, the numerical solutions are presented to show the applicability of the proposed method. Numerical results show that both the state and control variables converge at the end of the intended interval.

Keywords: Fuzzy fractional caputo derivative; Fuzzy fractional optimal control problem; Legendre basis function; Euler–Lagrange equations (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S1793005721500046

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