Numerical Solution of Some Types of Fractional Optimal Control Problems

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”...

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Bibliographic Details
Published in:TheScientificWorld 2013-01, Vol.2013 (2013), p.1-9
Main Authors: Sweilam, Nasser Hassan, Hoppe, Ronald H. W., Al-Ajami, Tamer Mostafa
Format: Article
Language:English
Subjects:
Applied mathematics
Approximation
Boundary value problems
Calculus
Chebyshev approximation
Control theory
Equations of state
Integrals
Mathematical research
Methods
Numerical analysis
Numerical integration
Optimal control
Optimization
Polynomials
Rayleigh-Ritz method
Spectral methods
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Summary: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.
ISSN:2356-6140
1537-744X
1537-744X
DOI:10.1155/2013/306237