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Optimal Control of Nonlinear Fractional-Order Systems with Multiple Time-Varying Delays

Author

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  • Chongyang Liu

    (Shandong Technology and Business University
    Curtin University)

  • Zhaohua Gong

    (Shandong Technology and Business University)

  • Kok Lay Teo

    (Sunway University
    Tianjin University of Finance and Economics)

  • Song Wang

    (Curtin University)

Abstract

This paper considers an optimal control problem governed by nonlinear fractional-order systems with multiple time-varying delays and subject to canonical constraints, where the fractional-order derivatives are expressed in the Caputo sense. To solve the problem by discretization scheme, an explicit numerical integration technique is proposed for solving the fractional-order system, and the trapezoidal rule is introduced to approximate the cost functional. Then, the gradients of the resulting cost and constraint functions are derived. On the basis of this result, we develop a gradient-based optimization algorithm to numerically solve the discretized problem. Finally, numerical results of several non-trivial examples are provided to illustrate the applicability and effectiveness of the proposed algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:193:y:2022:i:1:d:10.1007_s10957-021-01935-7
    DOI: 10.1007/s10957-021-01935-7
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    References listed on IDEAS

    as
    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. 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.
    3. Sayyed Mohammad Hoseini & Hamid Reza Marzban, 2016. "Costate Computation by an Adaptive Pseudospectral Method for Solving Optimal Control Problems with Piecewise Constant Time Lag," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 735-755, September.
    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).
    5. Pan Mu & Lei Wang & Chongyang Liu, 2020. "A Control Parameterization Method to Solve the Fractional-Order Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 234-247, October.
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    Cited by:

    1. Liu, Chongyang & Zhou, Tuo & Gong, Zhaohua & Yi, Xiaopeng & Teo, Kok Lay & Wang, Song, 2023. "Robust optimal control of nonlinear fractional systems," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    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.

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