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Optimal control of nonlinear fractional systems with multiple pantograph‐delays

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  • Gong, Zhaohua
  • Liu, Chongyang
  • Teo, Kok Lay
  • Yi, Xiaopeng

Abstract

In this paper, we consider optimal control of nonlinear fractional-order systems with multiple pantograph-delays, where the fractional-order derivatives are expressed in the Caputo sense. For this problem, we first propose an explicit integration scheme to numerically solve the nonlinear fractional-order system with multiple pantograph-delays and approximate the cost functional using the trapezoidal rule. This yields a series of nonlinear parameter optimization problems. Then, we derive gradients of the cost functions in the resulting problems. Furthermore, we present a gradient-based optimization approach to solve the fractional pantograph-delay optimal control problem. Finally, we validate the proposed solution approach by solving three numerical examples.

Suggested Citation

  • Gong, Zhaohua & Liu, Chongyang & Teo, Kok Lay & Yi, Xiaopeng, 2022. "Optimal control of nonlinear fractional systems with multiple pantograph‐delays," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    • Handle: RePEc:eee:apmaco:v:425:y:2022:i:c:s0096300322001783
    DOI: 10.1016/j.amc.2022.127094
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    References listed on IDEAS

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    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. 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).
    3. 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. 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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