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

Huan Ding, Jing Qian (), Danning Tian and Yun Zeng
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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

Mathematics, 2025, vol. 13, issue 5, 1-19

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.

Keywords: practical predefined-time control scheme; chaos synchronization; sliding mode control; norm-based adaptive rate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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