WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Publisher: search.filters.publisher.Sage Publications LtdSubject: search.filters.subject.Operational Matrix

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Now showing 1 - 5 of 5
  • Article
    Citation - WoS: 42
    Citation - Scopus: 44
    A Numerical Approach for Solving Fractional Optimal Control Problems With Mittag-Leffler Kernel
    (Sage Publications Ltd, 2022) Ganji, Roghayeh M.; Sayevand, Khosro; Baleanu, Dumitru; Jafari, Hossein
    In this work, we present a numerical approach based on the shifted Legendre polynomials for solving a class of fractional optimal control problems. The derivative is described in the Atangana-Baleanu derivative sense. To solve the problem, operational matrices of AB-fractional integration and multiplication, together with the Lagrange multiplier method for the constrained extremum, are considered. The method reduces the main problem to a system of nonlinear algebraic equations. In this framework by solving the obtained system, the approximate solution is calculated. An error estimate of the numerical solution is also proved for the approximate solution obtained by the proposed method. Finally, some illustrative examples are presented to demonstrate the accuracy and validity of the proposed scheme.
  • Article
    Citation - WoS: 86
    Citation - Scopus: 93
    Solving Multi-Dimensional Fractional Optimal Control Problems With Inequality Constraint by Bernstein Polynomials Operational Matrices
    (Sage Publications Ltd, 2013) Rostamy, Davood; Baleanu, Dumitru; Alipour, Mohsen
    In this paper, we present a method for solving multi-dimensional fractional optimal control problems. Firstly, we derive the Bernstein polynomials operational matrix for the fractional derivative in the Caputo sense, which has not been done before. The main characteristic behind the approach using this technique is that it reduces the problems to those of solving a system of algebraic equations, thus greatly simplifying the problem. The results obtained are in good agreement with the existing ones in the open literature and it is shown that the solutions converge as the number of approximating terms increases, and the solutions approach to classical solutions as the order of the fractional derivatives approach 1.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 7
    Chebyshev Cardinal Functions for a New Class of Nonlinear Optimal Control Problems With Dynamical Systems of Weakly Singular Variable-Order Fractional Integral Equations
    (Sage Publications Ltd, 2020) Mahmoudi, Mohammad Reza; Avazzadeh, Zakieh; Baleanu, Dumitru; Heydari, Mohammad Hossein
    The main objectives of this study are to introduce a new class of optimal control problems governed by a dynamical system of weakly singular variable-order fractional integral equations and to establish a computational method by utilizing the Chebyshev cardinal functions for their numerical solutions. In this way, a new operational matrix of variable-order fractional integration is generated for the Chebyshev cardinal functions. In the established method, first the control and state variables are approximated by the introduced basis functions. Then, the interpolation property of these basis functions together with their mentioned operational matrix is applied to derive an algebraic equation instead of the objective function and an algebraic system of equations instead of the dynamical system. Eventually, the constrained extrema technique is applied by adjoining the constraints generated from the dynamical system to the objective function using a set of Lagrange multipliers. The accuracy of the established approach is examined through several test problems. The obtained results confirm the high accuracy of the presented method.
  • Article
    Citation - WoS: 64
    Citation - Scopus: 69
    A Direct Numerical Solution of Time-Delay Fractional Optimal Control Problems by Using Chelyshkov Wavelets
    (Sage Publications Ltd, 2019) Mohammadi, F.; Baleanu, D.; Moradi, L.
    The aim of the present study is to present a numerical algorithm for solving time-delay fractional optimal control problems (TDFOCPs). First, a new orthonormal wavelet basis, called Chelyshkov wavelet, is constructed from a class of orthonormal polynomials. These wavelet functions and their properties are implemented to derive some operational matrices. Then, the fractional derivative of the state function in the dynamic constraint of TDFOCPs is approximated by means of the Chelyshkov wavelets. The operational matrix of fractional integration together with the dynamical constraints is used to approximate the control function directly as a function of the state function. Finally, these approximations were put in the performance index and necessary conditions for optimality transform the under consideration TDFOCPs into an algebraic system. Moreover, some illustrative examples are considered and the obtained numerical results were compared with those previously published in the literature.
  • Article
    Citation - WoS: 67
    Citation - Scopus: 82
    A Numerical Approach Based on Legendre Orthonormal Polynomials for Numerical Solutions of Fractional Optimal Control Problems
    (Sage Publications Ltd, 2017) Doha, E. H.; Baleanu, D.; Bhrawy, A. H.; Ezz-Eldien, S. S.
    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.