Numerical Solution of Some Types of Fractional Optimal Control Problems. (9th December 2013)

• Record Type: Journal Article
• Authors: Sweilam, Nasser Hassan; Al-Ajami, Tamer Mostafa; Hoppe, Ronald H. W.
• Other Names: Li C. Academic Editor.; Liu F. Academic Editor.; Magin R. Academic Editor.; Sikorskii A. Academic Editor.; Yuste S. B. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2013(2013)
• Publication Date: 2013-12-09
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2013/306237
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : We present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm "optimize first, then discretize" and relies on the approximation of the necessary optimality conditions in terms of the associated Hamiltonian. In the second approach, the state equation is discretized first using the Clenshaw and Curtis scheme for the numerical integration of nonsingular functions followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Two illustrative examples are included to demonstrate the validity and applicability of the suggested approaches.