An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index

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...

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Bibliographic Details
Main Author: Bhrawy, A. H. (author)
Other Authors: Doha, E.H. (author), Machado, J. A. Tenreiro (author), Ezz-Eldien, S. S. (author)
Format: article
Language:eng
Published: 2015
Subjects:
Fractional optimal control problem
Legendre polynomials
Operational matrix
Lagrange multiplier method
Caputo derivatives
Riemann–liouville integrals
Online Access:http://hdl.handle.net/10400.22/6964
Country:Portugal
Oai:oai:recipp.ipp.pt:10400.22/6964
Description
Summary: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.

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