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An Efficient Algorithm for the Multi-Scale Solution of Nonlinear Fractional Optimal Control Problems

Author

Listed:
  • Araz Noori Dalawi

    (Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz 5166616471, Iran)

  • Mehrdad Lakestani

    (Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz 5166616471, Iran)

  • Elmira Ashpazzadeh

    (Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz 5166616471, Iran)

Abstract

An efficient algorithm based on the wavelet collocation method is introduced in order to solve nonlinear fractional optimal control problems (FOCPs) with inequality constraints. By using the interpolation properties of Hermite cubic spline functions, we construct an operational matrix of the Caputo fractional derivative for the first time. Using this matrix, we reduce the nonlinear fractional optimal control problem to a nonlinear programming problem that can be solved with some suitable optimization algorithms. Illustrative examples are examined to demonstrate the important features of the new method.

Suggested Citation

  • Araz Noori Dalawi & Mehrdad Lakestani & Elmira Ashpazzadeh, 2022. "An Efficient Algorithm for the Multi-Scale Solution of Nonlinear Fractional Optimal Control Problems," Mathematics, MDPI, vol. 10(20), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3779-:d:941416
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    References listed on IDEAS

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    1. 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.
    2. Ali Lotfi & Sohrab Ali Yousefi, 2014. "Epsilon-Ritz Method for Solving a Class of Fractional Constrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 884-899, December.
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