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A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems

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dc.contributor.author Ezz-Eldien, S. S.
dc.contributor.author Doha, E. H.
dc.contributor.author Baleanu, Dumitru
dc.contributor.author Bhrawy, A. H.
dc.date.accessioned 2020-02-26T11:03:54Z
dc.date.available 2020-02-26T11:03:54Z
dc.date.issued 2017-01
dc.identifier.citation Ezz-Eldien, S. S...et al. (2017). "A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems", Journal Of Vibration And Control, Vol. 23, No.1, pp.16-30. tr_TR
dc.identifier.issn 1077-5463
dc.identifier.uri http://hdl.handle.net/20.500.12416/2505
dc.description.abstract 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. tr_TR
dc.language.iso eng tr_TR
dc.publisher Sage Publications LTD tr_TR
dc.relation.isversionof 10.1177/1077546315573916 tr_TR
dc.rights info:eu-repo/semantics/closedAccess tr_TR
dc.subject Fractional Optimal Control Problem tr_TR
dc.subject Legendre Polynomials tr_TR
dc.subject Operational Matrix tr_TR
dc.subject Lagrange Multiplier Method tr_TR
dc.subject Caputo Derivatives tr_TR
dc.title A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems tr_TR
dc.type article tr_TR
dc.relation.journal Journal Of Vibration And Control tr_TR
dc.contributor.authorID 56389 tr_TR
dc.identifier.volume 23 tr_TR
dc.identifier.issue 1 tr_TR
dc.identifier.startpage 16 tr_TR
dc.identifier.endpage 30 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü tr_TR


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