Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Doha, E. H.Subject: search.filters.subject.Fractional Optimal Control Problem

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 66
    Citation - Scopus: 63
    An Accurate Numerical Technique for Solving Fractional Optimal Control Problems
    (Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.; Abdelkawy, M. A.; Matematik
    In this article, we propose the shifted Legendre orthonormal polynomials for the numerical solution of the fractional optimal control problems that appear in several branches of physics and engineering. The Rayleigh-Ritz method for the necessary conditions of optimization and the operational matrix of fractional derivatives are used together with the help of the properties of the shifted Legendre orthonormal polynomials to reduce the fractional optimal control problem to solving a system of algebraic equations that greatly simplifies the problem. For confirming the efficiency and accuracy of the proposed technique, an illustrative numerical example is introduced with its approximate solution.
  • Article
    Citation - WoS: 49
    Citation - Scopus: 55
    Solving Fractional Optimal Control Problems Within a Chebyshev-Legendre Operational Technique
    (Taylor & Francis Ltd, 2017) Ezz-Eldien, S. S.; Doha, E. H.; Abdelkawy, M. A.; Baleanu, D.; Bhrawy, A. H.
    In this manuscript, we report a new operational technique for approximating the numerical solution of fractional optimal control (FOC) problems. The operational matrix of the Caputo fractional derivative of the orthonormal Chebyshev polynomial and the Legendre-Gauss quadrature formula are used, and then the Lagrange multiplier scheme is employed for reducing such problems into those consisting of systems of easily solvable algebraic equations. We compare the approximate solutions achieved using our approach with the exact solutions and with those presented in other techniques and we show the accuracy and applicability of the new numerical approach, through two numerical examples.
  • Article
    Citation - WoS: 67
    Citation - Scopus: 82
    A Numerical Approach Based on Legendre Orthonormal Polynomials for Numerical Solutions of Fractional Optimal Control Problems
    (Sage Publications Ltd, 2017) Doha, E. H.; Baleanu, D.; Bhrawy, A. H.; Ezz-Eldien, S. S.
    The numerical solution of a fractional optimal control problem having a quadratic performance index is proposed and analyzed. The performance index of the fractional optimal control problem is considered as a function of both the state and the control variables. The dynamic constraint is expressed as a fractional differential equation that includes an integer derivative in addition to the fractional derivative. The order of the fractional derivative is taken as less than one and described in the Caputo sense. Based on the shifted Legendre orthonormal polynomials, we employ the operational matrix of fractional derivatives, the Legendre-Gauss quadrature formula and the Lagrange multiplier method for reducing such a problem into a problem consisting of solving a system of algebraic equations. The convergence of the proposed method is analyzed. For confirming the validity and accuracy of the proposed numerical method, a numerical example is presented along with a comparison between our numerical results and those obtained using the Legendre spectral-collocation method.