An Efficient Numerical Scheme for Solving Multi-Dimensional Fractional Optimal Control Problems With a Quadratic Performance Index

被引：51

作者：

Bhrawy, A. H. ^{[1
,2
]}

Doha, E. H. ^{[3
]}

Tenreiro Machado, J. A. ^{[4
]}

Ezz-Eldien, S. S. ^{[5
]}

机构：

[1] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah, Saudi Arabia

[2] Beni Suef Univ, Fac Sci, Dept Math, Bani Suwayf, Egypt

[3] Cairo Univ, Fac Sci, Dept Math, Giza, Egypt

[4] Polytech Porto, Dept Elect Engn, Inst Engn, P-4200072 Oporto, Portugal

[5] Modern Acad, Inst Informat Technol, Dept Basic Sci, Cairo, Egypt

来源：

ASIAN JOURNAL OF CONTROL | 2015年 / 17卷 / 06期

关键词：

Fractional optimal control problem; legendre polynomials; operational matrix; lagrange multiplier method; caputo derivatives; riemann-liouville integrals; OPERATIONAL MATRIX; INTEGRATION; ORDER; EQUATIONS;

D O I：

10.1002/asjc.1109

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.

引用

页码：2389 / 2402

页数：14

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