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Multi-Sided Delayed Impulsive Feedback Method for Controlling Chaos and Reducing Loss Ratio in Switched Arrival System with Switching Time Greater than 0

Author

Listed:
  • Ming Chen

    (School of General Education, Hubei College of Chinese Medicine, Jingzhou 434020, China)

  • Xueshuai Zhu

    (School of Chemical and Environmental Engineering, China University of Mining and Technology, Beijing 100083, China)

Abstract

The switched arrival system is a typical hybrid system that is commonly used to simulate industrial control systems. The corresponding mathematical model and switching time are described. In order to be closer to the actual industrial control systems, the switching time is changed from 0 to greater than 0. In this case, the system not only generates chaos but also system losses. For this purpose, firstly, the causes of system losses are analyzed. Secondly, the Poincare section is selected to define the control target—periodic orbits. And then, the delayed impulsive feedback method is improved for the system at a switching time greater than 0, and extended to each boundary in order to enhance the control effect. This not only controls chaos in the system but also reduces the loss ratio and detects periodic orbits. Finally, numerical simulations of the system orbits and loss ratio with and without implementing control are compared. The possible intervals for the optimal control coefficient under the same initial conditions are detected. Period-1 orbits are detected at switching times greater than 0, and the stability of system operation is verified.

Suggested Citation

  • Ming Chen & Xueshuai Zhu, 2025. "Multi-Sided Delayed Impulsive Feedback Method for Controlling Chaos and Reducing Loss Ratio in Switched Arrival System with Switching Time Greater than 0," Mathematics, MDPI, vol. 13(2), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:198-:d:1563528
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    References listed on IDEAS

    as
    1. Ruofeng Rao & Quanxin Zhu, 2024. "Synchronization for Reaction–Diffusion Switched Delayed Feedback Epidemic Systems via Impulsive Control," Mathematics, MDPI, vol. 12(3), pages 1-12, January.
    2. Ruofeng Rao & Zhi Lin & Xiaoquan Ai & Jiarui Wu, 2022. "Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
    3. Fucheng Liao & Lijie Cui & Yanrong Lu & Jiamei Deng, 2020. "Preview Tracking Control of Linear Periodic Switched Systems with Dwell Time," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-9, October.
    4. Chun Zhang & Qiaoxia Tang & Zhixiang Wang, 2022. "Grazing and Symmetry-Breaking Bifurcations Induced Oscillations in a Switched System Composed of Duffing and van der Pol Oscillators," Mathematics, MDPI, vol. 10(5), pages 1-10, February.
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