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

dc.contributor.authorEzz-Eldien, S. S.
dc.contributor.authorDoha, E. H.
dc.contributor.authorBaleanu, Dumitru
dc.contributor.authorBhrawy, A. H.
dc.contributor.authorID56389tr_TR
dc.date.accessioned2020-02-26T11:03:54Z
dc.date.available2020-02-26T11:03:54Z
dc.date.issued2017
dc.departmentÇankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümüen_US
dc.description.abstractThe 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.en_US
dc.description.publishedMonth1
dc.identifier.citationEzz-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.en_US
dc.identifier.doi10.1177/1077546315573916
dc.identifier.endpage30en_US
dc.identifier.issn1077-5463
dc.identifier.issue1en_US
dc.identifier.startpage16en_US
dc.identifier.urihttp://hdl.handle.net/20.500.12416/2505
dc.identifier.volume23en_US
dc.language.isoenen_US
dc.publisherSage Publications LTDen_US
dc.relation.ispartofJournal Of Vibration And Controlen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectFractional Optimal Control Problemen_US
dc.subjectLegendre Polynomialsen_US
dc.subjectOperational Matrixen_US
dc.subjectLagrange Multiplier Methoden_US
dc.subjectCaputo Derivativesen_US
dc.titleA numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problemstr_TR
dc.titleA Numerical Approach Based on Legendre Orthonormal Polynomials for Numerical Solutions of Fractional Optimal Control Problemsen_US
dc.typeArticleen_US
dspace.entity.typePublication

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