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A Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems

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dc.contributor.author Agrawal, Om. P.
dc.contributor.author Baleanu, Dumitru
dc.date.accessioned 2020-04-08T21:31:09Z
dc.date.available 2020-04-08T21:31:09Z
dc.date.issued 2007-09
dc.identifier.citation Agrawal, O.P.; Baleanu, D., "A Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems", Journal Of Vibration And Control, Vol.13, No.9-10, pp.1269-1281, (2007). tr_TR
dc.identifier.issn 1077-5463
dc.identifier.uri http://hdl.handle.net/20.500.12416/2993
dc.description.abstract This paper deals with a direct numerical technique for Fractional Optimal Control Problems (FOCPs). In this paper, we formulate the FOCPs in terms of Riemann-Liouville Fractional Derivatives (RLFDs). It is demonstrated that right RLFDs automatically arise in the formulation even when the dynamics of the system is described using left RLFDs only. For numerical computation, the FDs are approximated using the Grunwald-Letnikov definition. This leads to a set of algebraic equations that can be solved using numerical techniques. Two examples, one time-invariant and the other time-variant, are considered to demonstrate the effectiveness of the formulation. Results show that as the order of the derivative approaches an integer value, these formulations lead to solutions for integer order system. The approach requires dividing of the entire time domain into several sub-domains. Further, as the sizes of the sub-domains are reduced, the solutions converge to unique solutions. However, the convergence is slow. A scheme that improves the convergence rate will be considered in a future paper. Other issues to be considered in the future include formulations using other types of derivatives, nonlinear and stochastic fractional optimal controls, existence and uniqueness of the solutions, and the error analysis. tr_TR
dc.language.iso eng tr_TR
dc.publisher Sage Publications LTD tr_TR
dc.relation.isversionof 10.1177/1077546307077467 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 Fractional Optimal Control tr_TR
dc.subject Fractional Euler-Lagrange Equations tr_TR
dc.title A Hamiltonian formulation and a direct 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.identifier.volume 13 tr_TR
dc.identifier.issue 9-10 tr_TR
dc.identifier.startpage 1269 tr_TR
dc.identifier.endpage 1281 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü tr_TR


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