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A Pseudospectral Method for Fractional Optimal Control Problems

Author

Listed:
  • Nastaran Ejlali

    (Tarbiat Modares University)

  • Seyed Mohammad Hosseini

    (Tarbiat Modares University)

Abstract

In this article, a direct pseudospectral method based on Lagrange interpolating functions with fractional power terms is used to solve the fractional optimal control problem. As most applied fractional problems have solutions in terms of the fractional power, using appropriate characteristic nodal-based functions with suitable power leads to a more accurate pseudospectral approximation of the solution. The Lagrange interpolating functions and their fractional derivatives belong to the Müntz space; such functions are employed to show that a relationship exists between the Karush–Kukn–Tucker conditions associated with nonlinear programming and the first optimal necessary conditions. Furthermore, the convergence of the method is investigated. The obtained numerical results are an indication of the behavior of the algorithm.

Suggested Citation

  • Nastaran Ejlali & Seyed Mohammad Hosseini, 2017. "A Pseudospectral Method for Fractional Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 83-107, July.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:1:d:10.1007_s10957-016-0936-8
    DOI: 10.1007/s10957-016-0936-8
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    Citations

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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. Heydari, M.H. & Razzaghi, M., 2021. "Piecewise Chebyshev cardinal functions: Application for constrained fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Pourbabaee, Marzieh & Saadatmandi, Abbas, 2022. "A new operational matrix based on Müntz–Legendre polynomials for solving distributed order fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 210-235.
    4. 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.
    5. Heydari, M.H. & Razzaghi, M., 2021. "A numerical approach for a class of nonlinear optimal control problems with piecewise fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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