A numerical technique for solving fractional optimal control problems

被引：171

作者：

Lotfi, A. ^{[2
]}

Dehghan, Mehdi ^{[1
]}

Yousefi, S. A. ^{[2
]}

机构：

[1] Amir Kabir Univ Technol, Dept Appl Math, Fac Math & Comp Sci, Tehran, Iran

[2] Shahid Beheshti Univ, Dept Math, Gc Tehran, Iran

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 62卷 / 03期

关键词：

Fractional optimal control problem; Caputo fractional derivative; Legendre polynomial basis; Operational matrix; Lagrange multiplier method; HOMOTOPY ANALYSIS METHOD; EQUATIONS; CALCULUS; FORMULATION; SCHEME;

D O I：

10.1016/j.camwa.2011.03.044

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a numerical method for solving a class of fractional optimal control problems (FOCPs). The fractional derivative in these problems is in the Caputo sense. The method is based upon the Legendre orthonormal polynomial basis. The operational matrices of fractional Riemann-Liouville integration and multiplication, along with the Lagrange multiplier method for the constrained extremum are considered. By this method, the given optimization problem reduces to the problem of solving a system of algebraic equations. By solving this system, we achieve the solution of the FOCP. Illustrative examples are included to demonstrate the validity and applicability of the new technique. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1055 / 1067

页数：13

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