Matematik Bölümü Yayın Koleksiyonu

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  • Article
    Citation - WoS: 20
    Citation - Scopus: 23
    A Numerical Scheme for Two-Dimensional Optimal Control Problems With Memory Effect
    (Pergamon-elsevier Science Ltd, 2010) Defterli, Ozlem
    A new formulation for multi-dimensional fractional optimal control problems is presented in this article. The fractional derivatives which are coming from the formulation of the problem are defined in the Riemann-Liouville sense. Some terminal conditions are imposed on the state and control variables whose dimensions need not be the same. A numerical scheme is described by using the Grunwald-Letnikov definition to approximate the Riemann-Liouville Fractional Derivatives. The set of fractional differential equations, which are obtained after the discretization of the time domain, are solved within the Grunwald-Letnikov approximation to obtain the state and the control variable numerically. A two-dimensional fractional optimal control problem is studied as an example to demonstrate the performance of the scheme. (C) 2009 Elsevier Ltd. All rights reserved.