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Norm-Based Adaptive Control with a Novel Practical Predefined-Time Sliding Mode for Chaotic System Synchronization

Author

Listed:
  • Huan Ding

    (School of Metallurgy and Energy Engineering, Kunming University of Science and Technology, Kunming 650093, China)

  • Jing Qian

    (School of Metallurgy and Energy Engineering, Kunming University of Science and Technology, Kunming 650093, China)

  • Danning Tian

    (School of Global Public Health, New York University, New York, NY 10012, USA)

  • Yun Zeng

    (School of Metallurgy and Energy Engineering, Kunming University of Science and Technology, Kunming 650093, China)

Abstract

This paper proposes a novel, practical, predefined-time control theory for chaotic system synchronization under external disturbances and modeling uncertainties. Based on this theory, a robust sliding mode surface is designed to minimize chattering on a sliding surface, enhancing system stability. Additionally, a norm-based adaptive control strategy is developed to dynamically adjust control gains, ensuring system convergence to the equilibrium point within the predefined time. Theoretical analysis guarantees predefined-time stability using a Lyapunov framework. Numerical simulations on the Chen and multi-wing chaotic Lu systems demonstrate the proposed method’s superior convergence speed, precision, and robustness, highlighting its applicability to complex systems.

Suggested Citation

  • Huan Ding & Jing Qian & Danning Tian & Yun Zeng, 2025. "Norm-Based Adaptive Control with a Novel Practical Predefined-Time Sliding Mode for Chaotic System Synchronization," Mathematics, MDPI, vol. 13(5), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:748-:d:1599378
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    References listed on IDEAS

    as
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    4. Wang, Leimin & Dong, Tiandu & Ge, Ming-Feng, 2019. "Finite-time synchronization of memristor chaotic systems and its application in image encryption," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 293-305.
    5. Gong, Li-Hua & Luo, Hui-Xin & Wu, Rou-Qing & Zhou, Nan-Run, 2022. "New 4D chaotic system with hidden attractors and self-excited attractors and its application in image encryption based on RNG," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    6. Deepika, Deepika & Kaur, Sandeep & Narayan, Shiv, 2018. "Uncertainty and disturbance estimator based robust synchronization for a class of uncertain fractional chaotic system via fractional order sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 196-203.
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    Full references (including those not matched with items on IDEAS)

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