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Fractional-order Bessel wavelet functions for solving variable order fractional optimal control problems with estimation error

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  • Haniye Dehestani
  • Yadollah Ordokhani
  • Mohsen Razzaghi

Abstract

In the present paper, we apply the fractional-order Bessel wavelets (FBWs) for solving optimal control problems with variable-order (VO) fractional dynamical system. The VO fractional derivative operator is proposed in the sense of Caputo type. To solve the considered problem, the collocation method based on FBWFs, pseudo-operational matrix of VO fractional derivative and the dual operational matrix is proposed. In fact, we convert the problem with unknown coefficients in the constraint equations, performance index and conditions to an optimisation problem, by utilising the proposed method. Also, the convergence of the method with details is discussed. At last, to demonstrate the high precision of the numerical approach, we examine several examples.

Suggested Citation

  • Haniye Dehestani & Yadollah Ordokhani & Mohsen Razzaghi, 2020. "Fractional-order Bessel wavelet functions for solving variable order fractional optimal control problems with estimation error," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(6), pages 1032-1052, April.
    • Handle: RePEc:taf:tsysxx:v:51:y:2020:i:6:p:1032-1052
    DOI: 10.1080/00207721.2020.1746980
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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. Dehestani, H. & Ordokhani, Y. & Razzaghi, M., 2020. "Application of fractional Gegenbauer functions in variable-order fractional delay-type equations with non-singular kernel derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Hari M. Srivastava & Kush Kumar Mishra & Santosh K. Upadhyay, 2022. "Characterizations of Continuous Fractional Bessel Wavelet Transforms," Mathematics, MDPI, vol. 10(17), pages 1-11, August.
    4. 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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