An Efficient Numerical Scheme for Solving Multi‐Dimensional Fractional Optimal Control Problems With a Quadratic Performance Index. Issue 6 (4th March 2015)

• Record Type: Journal Article
• Authors: Bhrawy, A. H.; Doha, E. H.; Tenreiro Machado, J. A.; Ezz‐Eldien, S. S.
• Is Part Of: Asian journal of control. Volume 17:Issue 6(2015:Nov.)
• Page Start: 2389
• Page End: 2402
• Publication Date: 2015-03-04
• Subjects: Fractional optimal control problem -- legendre polynomials -- operational matrix -- lagrange multiplier method -- caputo derivatives -- riemann–liouville integrals; Automatic control -- Periodicals; Control theory -- Periodicals; 629.805
• DOI: 10.1002/asjc.1109
• Languages: English
• ISSNs: 1561-8625

Abstract

Abstract: 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.