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A Combination of Variational and Penalty Methods for Solving a Class of Fractional Optimal Control Problems

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  • Ali Lotfi

    (Shahid Beheshti University, G.C.)

Abstract

This paper develops an approximate method, based on the combination of epsilon penalty and variational methods, for solving a class of multidimensional fractional optimal control problems. The fractional derivative is in the Caputo sense. In the presented method, utilizing the epsilon method, the given optimal control problem transforms into an unconstrained optimization problem; then, the equivalent variational equality is derived for the given unconstrained problem. The variational equality is approximately solved by applying a spectral method.

Suggested Citation

  • Ali Lotfi, 2017. "A Combination of Variational and Penalty Methods for Solving a Class of Fractional Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 65-82, July.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:1:d:10.1007_s10957-017-1106-3
    DOI: 10.1007/s10957-017-1106-3
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    References listed on IDEAS

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    1. Tian Liang Guo, 2013. "The Necessary Conditions of Fractional Optimal Control in the Sense of Caputo," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 115-126, January.
    2. Ali Lotfi & Sohrab Ali Yousefi, 2014. "Epsilon-Ritz Method for Solving a Class of Fractional Constrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 884-899, December.
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    Cited by:

    1. Marzban, Hamid Reza, 2022. "A generalization of Müntz-Legendre polynomials and its implementation in optimal control of nonlinear fractional delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Tim Chen & Bunnitru Daleanu & J. C.-Y. Chen*, 2018. "On the Fractional Optimal Control Problems with Singular and Non–Singular Derivative Operators: A Mathematical Derive," Scientific Review, Academic Research Publishing Group, vol. 4(12), pages 95-98, 12-2018.
    3. Dumitru Baleanu & Amin Jajarmi & Mojtaba Hajipour, 2017. "A New Formulation of the Fractional Optimal Control Problems Involving Mittag–Leffler Nonsingular Kernel," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 718-737, December.

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