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' 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 non-singular 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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Author:Nasser H. Sweilam, Tamer M. Al-Ajmi, Ronald H. W. HoppeGND
Frontdoor URL
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2013-20)
Publishing Institution:Universität Augsburg
Contributing Corporation:Cairo University
Release Date:2013/11/06
Tag:fractional calculus; fractional optimal control; numerical solution; Chebyshev spectral method
GND-Keyword:Gebrochene Analysis; Optimale Kontrolle; Numerisches Verfahren; Spektralmethode
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand