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Numerical Solution of Fractional Optimal Control

Author

Listed:
  • Wen Li

    (Curtin University)

  • Song Wang

    (Curtin University)

  • Volker Rehbock

    (Curtin University)

Abstract

This paper presents a numerical algorithm for solving a class of nonlinear optimal control problems subject to a system of fractional differential equations. We first propose a robust second-order numerical integration scheme for the system. The objective is approximated by the trapezoidal rule. We then apply a gradient-based optimization method to the discretized problem. Formulas for calculating the gradients are derived. Computational results demonstrate that our method is able to generate accurate numerical approximations for problems with multiple states and controls. It is also robust with respect to the fractional orders of derivatives.

Suggested Citation

  • Wen Li & Song Wang & Volker Rehbock, 2019. "Numerical Solution of Fractional Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 556-573, February.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:2:d:10.1007_s10957-018-1418-y
    DOI: 10.1007/s10957-018-1418-y
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    References listed on IDEAS

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    1. Neelam Singha & Chandal Nahak, 2017. "An Efficient Approximation Technique for Solving a Class of Fractional Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 785-802, September.
    2. Chen, Wen & Wang, Song, 2017. "A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 174-187.
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    Citations

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    Cited by:

    1. Chongyang Liu & Zhaohua Gong & Changjun Yu & Song Wang & Kok Lay Teo, 2021. "Optimal Control Computation for Nonlinear Fractional Time-Delay Systems with State Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 83-117, October.
    2. Chongyang Liu & Changjun Yu & Zhaohua Gong & Huey Tyng Cheong & Kok Lay Teo, 2023. "Numerical Computation of Optimal Control Problems with Atangana–Baleanu Fractional Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 798-816, May.
    3. Chongyang Liu & Zhaohua Gong & Kok Lay Teo & Song Wang, 2022. "Optimal Control of Nonlinear Fractional-Order Systems with Multiple Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 856-876, June.
    4. Gong, Zhaohua & Liu, Chongyang & Teo, Kok Lay & Wang, Song & Wu, Yonghong, 2021. "Numerical solution of free final time fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 405(C).

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