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Extended Chebyshev cardinal wavelets for nonlinear fractional delay optimal control problems

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  • M. H. Heydari
  • M. Razzaghi

Abstract

In this study, a new family of cardinal wavelets called the extended Chebyshev cardinal wavelets is introduced to investigate problems on arbitrary finite domains. These wavelets possess many beneficial properties, such as spectral (exponential) accuracy, cardinality and orthogonality. The classical and fractional derivative matrices together with the fractional integral matrix of these wavelets are obtained. Two formulations of delay optimal control problems with a dynamical system involved with fractional derivatives are introduced. Two direct approaches based on these wavelets, together with their fractional derivative and integral matrices, are adopted for solving such problems. The presented methods transform solving the problems under study into solving constrained minimisation problems by approximating the state and control variables via the expressed wavelets. Some numerical examples are provided to show the efficiency of the expressed wavelet methods.

Suggested Citation

  • M. H. Heydari & M. Razzaghi, 2022. "Extended Chebyshev cardinal wavelets for nonlinear fractional delay optimal control problems," International Journal of Systems Science, Taylor & Francis Journals, vol. 53(5), pages 1048-1067, April.
    • Handle: RePEc:taf:tsysxx:v:53:y:2022:i:5:p:1048-1067
    DOI: 10.1080/00207721.2021.1987579
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    Cited by:

    1. Sabermahani, Sedigheh & Ordokhani, Yadollah & Rahimkhani, Parisa, 2023. "Application of generalized Lucas wavelet method for solving nonlinear fractal-fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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