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ScientificWorldJournal. 2013 Dec 9;2013:306237. doi: 10.1155/2013/306237. eCollection 2013.

Numerical solution of some types of fractional optimal control problems.

Author information

1
Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt.
2
Institute of Mathematics, University of Augsburg, 86159 Augsburg, Germany ; Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA.

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.

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