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Dynamic Optimization of Nonlinear Fractional Impulsive Switched Systems

Author

Listed:
  • Chongyang Liu

    (Shandong Technology and Business University)

  • Zhaohua Gong

    (Curtin University)

  • Yonghong Wu

    (Curtin University)

  • Benchawan Wiwatanapataphee

    (Curtin University)

  • Kok Lay Teo

    (Sunway University)

Abstract

Optimization of fractional impulsive switched systems has various applications. In this paper, we address the dynamic optimization problem of a class of fractional impulsive switched systems, where a set of system parameters and the switching instants are decision variables to minimize a given cost functional. For this problem, we first convert these variable switching instants into the fixed instants in a new time horizon by using a proposed time-scaling transformation. This gives rise to an equivalent optimization problem with the fixed switching instants. Then, we prove that the cost functional’s gradients can be represented by the solutions of a series of auxiliary fractional impulsive systems. Furthermore, numerical schemes for solving the equivalent and auxiliary fractional impulsive system are presented. On this basis, we develop a gradient-based optimization approach to solve the dynamic optimization problem. At last, numerical results of three non-trivial examples illustrate the applicability and effectiveness of the developed optimization approach.

Suggested Citation

  • Chongyang Liu & Zhaohua Gong & Yonghong Wu & Benchawan Wiwatanapataphee & Kok Lay Teo, 2025. "Dynamic Optimization of Nonlinear Fractional Impulsive Switched Systems," Journal of Optimization Theory and Applications, Springer, vol. 205(3), pages 1-23, June.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:3:d:10.1007_s10957-025-02675-8
    DOI: 10.1007/s10957-025-02675-8
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    References listed on IDEAS

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    1. Luo, Lingao & Li, Lulu & Huang, Wei, 2024. "Asymptotic stability of fractional-order Hopfield neural networks with event-triggered delayed impulses and switching effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 491-504.
    2. Sudsutad, Weerawat & Ahmad, Bashir & Ntouyas, Sotiris K. & Tariboon, Jessada, 2016. "Impulsively hybrid fractional quantum Langevin equation with boundary conditions involving Caputo qk-fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 47-62.
    3. Kok Lay Teo & Bin Li & Changjun Yu & Volker Rehbock, 2021. "Applied and Computational Optimal Control," Springer Optimization and Its Applications, Springer, number 978-3-030-69913-0, December.
    Full references (including those not matched with items on IDEAS)

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