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Numerical solution of free final time fractional optimal control problems

Author

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  • Gong, Zhaohua
  • Liu, Chongyang
  • Teo, Kok Lay
  • Wang, Song
  • Wu, Yonghong

Abstract

The main purpose of this work is to develop a numerical solution method for solving a class of nonlinear free final time fractional optimal control problems. This problem is subject to equality and inequality constraints in canonical forms, and the orders in the fractional system can be different. For this problem, we first show that, by a time-scaling transformation, the problem can be transformed into an equivalent fractional optimal control problem with fixed final time. We then discretize the transformed fractional optimal control problem by a second-order one-point numerical integration scheme and the trapezoidal rule. Furthermore, we derive the gradient formulae of the cost and constraint functions with respect to decision variables and propose a numerical procedure for calculating these gradients. On this basis, a gradient-based optimization algorithm is developed for solving the resulting problem. Finally, numerical simulations of three example problems illustrate the effectiveness of the developed algorithm.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:405:y:2021:i:c:s0096300321003593
    DOI: 10.1016/j.amc.2021.126270
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    References listed on IDEAS

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    1. 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.
    2. Shiri, B. & Baleanu, D., 2019. "System of fractional differential algebraic equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 203-212.
    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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    Citations

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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.
    2. 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.
    3. 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).
    4. 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.

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