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Piecewise Chebyshev cardinal functions: Application for constrained fractional optimal control problems

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  • Heydari, M.H.
  • Razzaghi, M.

Abstract

In this paper, a new set of basis functions called the piecewise Chebyshev cardinal functions is generated to investigate a class of constrained fractional optimal control problems. These basis functions possess many useful properties, such as orthogonality, cardinality and spectral accuracy. The fractional integral matrix of these functions is obtained. A direct scheme based on the these basis functions together with their fractional integral matrix is developed for solving the problem under consideration. The established method transforms solving the original problem into solving a constrained minimization problem by approximating the state and control variables in terms of the piecewise Chebyshev cardinal functions. Some numerical examples are given to show the efficiency of the proposed technique.

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  • Heydari, M.H. & Razzaghi, M., 2021. "Piecewise Chebyshev cardinal functions: Application for constrained fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004720
    DOI: 10.1016/j.chaos.2021.111118
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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. Shah, Kamal & Alqudah, Manar A. & Jarad, Fahd & Abdeljawad, Thabet, 2020. "Semi-analytical study of Pine Wilt Disease model with convex rate under Caputo–Febrizio fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    3. 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.
    4. Heydari, M.H. & Hooshmandasl, M.R. & Maalek Ghaini, F.M. & Cattani, C., 2016. "Wavelets method for solving fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 139-154.
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    Cited by:

    1. Heydari, M.H. & Razzaghi, M. & Rouzegar, J., 2022. "Chebyshev cardinal polynomials for delay distributed-order fractional fourth-order sub-diffusion equation," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Heydari, M.H. & Razzaghi, M., 2023. "Piecewise fractional Chebyshev cardinal functions: Application for time fractional Ginzburg–Landau equation with a non-smooth solution," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    3. 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).
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    5. 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).
    6. 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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