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A central difference numerical scheme for fractional optimal control problems

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dc.contributor.author Baleanu, Dumitru
dc.contributor.author Defterli, Özlem
dc.contributor.author Agrawal, Om. P.
dc.date.accessioned 2020-04-02T10:43:06Z
dc.date.available 2020-04-02T10:43:06Z
dc.date.issued 2009-04
dc.identifier.citation Baleanu, Dumitru; Defterli, Özlem; Agrawal, Om.P., "A central difference numerical scheme for fractional optimal control problems", Journal Of Vibration And Control, Vol.15, No.4, pp.583-597, (2009). tr_TR
dc.identifier.issn 1077-5463
dc.identifier.uri http://hdl.handle.net/20.500.12416/2829
dc.description.abstract This paper presents a modified numerical scheme for a class of fractional optimal control problems where a fractional derivative (FD) is defined in the Riemann-Liouville sense. In this scheme, the entire time domain is divided into several sub-domains, and a FD at a time node point is approximated using a modified Grunwald-Letnikov approach. For the first-order derivative, the proposed modified Grunwald-Letnikov definition leads to a central difference scheme. When the approximations are substituted into the fractional optimal control equations, it leads to a set of algebraic equations which are solved using a direct numerical technique. Two examples, one time-invariant and the other time-variant, are considered to study the performance of the numerical scheme. Results show that 1) as the order of the derivative approaches an integer value, these formulations lead to solutions for the integer-order system, and 2) as the sizes of the sub-domains are reduced, the solutions converge. It is hoped that the present scheme would lead to stable numerical methods for fractional differential equations and optimal control problems. tr_TR
dc.language.iso eng tr_TR
dc.publisher Sage Publications LTD tr_TR
dc.relation.isversionof 10.1177/1077546308088565 tr_TR
dc.rights info:eu-repo/semantics/closedAccess tr_TR
dc.subject Fractional Calculus tr_TR
dc.subject Riemann-Liouville Fractional Derivatives tr_TR
dc.subject Modified Grunwald-Letnikov Approximation tr_TR
dc.subject Fractional Optimal Control tr_TR
dc.title A central difference numerical scheme for 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.contributor.authorID 31401 tr_TR
dc.identifier.volume 15 tr_TR
dc.identifier.issue 4 tr_TR
dc.identifier.startpage 583 tr_TR
dc.identifier.endpage 597 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü tr_TR


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