Title : ( A Numerical Solution for Fractional Linear Quadratic Optimal Control Problems via Shifted Legendre Polynomials )
Authors: Saeed Nezhadhosein , Reza Ghanbari , Khatere Ghorbani-Moghadam ,
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Abstract
This paper presents a numerical indirect method based on shifted Legendre polynomials for solving fractional linear quadratic time-variant optimal control problems (FLQTVOCPs) in the Caputo sense. At first, using the well-known optimality conditions for FLQTVOCPs, a fractional two-point boundary value problem (FBVP) is obtained. For solving the FBVP, we introduce a new operational matrix of Riemann–Liouville fractional integrals based on the shifted Legendre polynomial, and then we show that an approximate solution can be computed by solving only an algebraic system of equations. Numerical experiments confirm the efficiency and accuracy of our proposed method.
Keywords
, Fractional calculus, Linear qudratic time variant system, Optimal control problem, Legendre orthogonal polynomials
@article{paperid:1090917,
author = {Saeed Nezhadhosein and Ghanbari, Reza and Khatere Ghorbani-Moghadam},
title = {A Numerical Solution for Fractional Linear Quadratic Optimal Control Problems via Shifted Legendre Polynomials},
journal = {International Journal of Applied and Computational Mathematics},
year = {2022},
volume = {8},
number = {4},
month = {June},
issn = {2349-5103},
keywords = {Fractional calculus; Linear qudratic time variant system; Optimal control
problem; Legendre orthogonal polynomials},
}
%0 Journal Article
%T A Numerical Solution for Fractional Linear Quadratic Optimal Control Problems via Shifted Legendre Polynomials
%A Saeed Nezhadhosein
%A Ghanbari, Reza
%A Khatere Ghorbani-Moghadam
%J International Journal of Applied and Computational Mathematics
%@ 2349-5103
%D 2022
