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A numerical approach for a class of nonlinear optimal control problems with piecewise fractional derivative

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  • Heydari, M.H.
  • Razzaghi, M.

Abstract

In this study, a kind of piecewise fractional derivatives based on the Caputo fractional derivative is used to define a novel category of fractional optimal control problems. The piecewise Chebyshev cardinal functions as an appropriate family of basis functions are considered to construct a numerical method for solving such problems. The classical and piecewise fractional derivative matrices of these basis functions are derived and used in constructing the proposed technique. The established scheme transforms obtaining the solution of such problems into finding the solution of algebraic systems of equations by approximating the state and control variables using the mentioned basis functions. The accuracy of the expressed approach is investigated by solving some examples.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921008195
    DOI: 10.1016/j.chaos.2021.111465
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    References listed on IDEAS

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    1. Heydari, M.H., 2020. "Chebyshev cardinal functions for a new class of nonlinear optimal control problems generated by Atangana–Baleanu–Caputo variable-order fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    2. Li, Ming, 2020. "Multi-fractional generalized Cauchy process and its application to teletraffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    3. Heydari, M.H. & Razzaghi, M., 2021. "Piecewise Chebyshev cardinal functions: Application for constrained fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    4. Atangana, Abdon & İğret Araz, Seda, 2021. "New concept in calculus: Piecewise differential and integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. 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.
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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. Zhao, Yanwei & Wang, Huanqing & Xu, Ning & Zong, Guangdeng & Zhao, Xudong, 2023. "Reinforcement learning-based decentralized fault tolerant control for constrained interconnected nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    3. Marzban, Hamid Reza & Nezami, Atiyeh, 2022. "Analysis of nonlinear fractional optimal control systems described by delay Volterra–Fredholm integral equations via a new spectral collocation method," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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