Adaptive Event-Triggered Control of Time-Varying Nonlinear Systems: A Tight and Powerful Strategy

Lei Chu; Yungang Liu

doi:10.1109/JAS.2025.125786

Volume 12 Issue 11

Nov. 2025

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 19.2, Top 1 (SCI Q1)

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2025 > 12(11): 2194-2206

L. Chu and Y. Liu, “Adaptive event-triggered control of time-varying nonlinear systems: A tight and powerful strategy,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 11, pp. 2194–2206, Nov. 2025. doi: 10.1109/JAS.2025.125786

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L. Chu and Y. Liu, “Adaptive event-triggered control of time-varying nonlinear systems: A tight and powerful strategy,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 11, pp. 2194–2206, Nov. 2025. doi: 10.1109/JAS.2025.125786

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Adaptive Event-Triggered Control of Time-Varying Nonlinear Systems: A Tight and Powerful Strategy

doi: 10.1109/JAS.2025.125786

Lei Chu^,,
Yungang Liu^{,
,}

Funds: This work was supported in part by the National Natural Science Foundation of China (62033007) and the Fundamental Research Program of Shandong Province (ZR2023ZD37)

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Author Bio:
Lei Chu received B.S. and M.S. degrees in mathematics from Qingdao University of Science and Technology in 2014 and 2018, respectively. She is pursuing the Ph.D. degree in control theory and control engineering from Shandong University

Yungang Liu received the Ph.D. degree in control theory and control engineering from Shanghai JiaoTong University in 2000. He is currently the Changjiang Scholar Chair Professor with the School of Control Science and Engineering, Shandong University (SDU). He is the Director of the Key Laboratory of Machine Intelligence and System Control, Ministry of Education of China; the Director of the Institute of Artificial Intelligence and Systems and Control, SDU; the Director of the Technical Committee on Artificial Intelligence and Machine Vision, Shandong Institute of Electronics; and the Director of the SDU-IBM Research Center on Big Data and Analytics. He is also the Vice Director of the Engineering Research Center of Intelligent Unmanned Systems, Ministry of Education of China. His current research interests include stochastic control, nonlinear control design and system analysis, cooperative control, distributed parameter systems, adaptive control and applications, robots and motion control, and artificial intelligence. He was a recipient of the National Outstanding Youth Science Foundation of China, the Special Government Allowances of State Council of China, Taishan Scholar Climbing Professor of Shandong Province of China, the Guan Zhaozhi Award in Chinese Control Conference in 2004, the Second Prize of the National Natural Science Award of China in 2015, the Excellent Doctoral Dissertation Award of Chinese Association of Automation (CAA) in 2018, and the Outstanding Graduate Student Instructor Awards of Shandong University and Shandong Province in 2019 and 2021
Corresponding author: Yungang Liu, e-mail: lygfr@sdu.edu.cn
¹ The “radius” \begin{document}$ \delta_{{\theta}} $\end{document} means \begin{document}$ \frac{1}{2}\|\bar{\theta}-\underline{{\theta}}\| $\end{document}, where \begin{document}$ \bar{\theta} $\end{document} and \begin{document}$ \underline{{\theta}} $\end{document} are the unknown upper and lower bound of Θ, respectively.
² The “average” of time-varying parameter (vector) \begin{document}$ {\theta}(t) $\end{document} means \begin{document}$ \frac{1}{2}\|\bar {\theta}+\underline{{\theta}}\| $\end{document}, where \begin{document}$ \bar {\theta} $\end{document} and \begin{document}$ \underline{{\theta}} $\end{document} are the unknown upper and lower bounds of \begin{document}$ {\theta}(t) $\end{document}, respectively.
Received Date: 2025-04-16
Revised Date: 2025-06-20
Accepted Date: 2025-08-06

Available Online: 2025-11-21

Abstract

Abstract

This paper considers adaptive event-triggered stabilization for a class of uncertain time-varying nonlinear systems. Remarkably, the systems contain intrinsic time-varying unknown parameters which are allowed to be non-differentiable and in turn can be fast-varying. Moreover, the systems admit unknown control directions. To counteract the different uncertainties, more than one compensation mechanism has to be incorporated. However, in the context of event-triggered control, ensuring the effectiveness of these compensation mechanisms under reduced execution necessitates delicate design and analysis. This paper proposes a tight and powerful strategy for adaptive event-triggered control (ETC) by integrating the state-of-the-art adaptive techniques. In particular, the strategy substantially mitigates the conservatism caused by repetitive inequality-based treatments of uncertainties. Specifically, by leveraging the congelation-of-variables method and tuning functions, the conservatism in the treatment of the fast-varying parameters is significantly reduced. With multiple Nussbaum functions employed to handle unknown control directions, a set of dynamic compensations is designed to counteract unknown amplitudes of control coefficients without relying on inequality-based treatments. Moreover, a dedicated dynamic compensation is introduced to deal with the control coefficient coupled with the execution error, based on which a relative-threshold event-triggering mechanism (ETM) is rigorously validated. It turns out that the adaptive event-triggered controller achieves the closed-loop convergence while guaranteeing a uniform lower bound for inter-execution times. Simulation results verify the effectiveness and superiority of the proposed strategy.
- Adaptive event-triggered control,
- multiple Nussbaum functions,
- nonlinear systems,
- time-varying uncertainties

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¹ The “radius” $ \delta_{{\theta}} $ means $ \frac{1}{2}\|\bar{\theta}-\underline{{\theta}}\| $, where $ \bar{\theta} $ and $ \underline{{\theta}} $ are the unknown upper and lower bound of Θ, respectively.
² The “average” of time-varying parameter (vector) $ {\theta}(t) $ means $ \frac{1}{2}\|\bar {\theta}+\underline{{\theta}}\| $, where $ \bar {\theta} $ and $ \underline{{\theta}} $ are the unknown upper and lower bounds of $ {\theta}(t) $, respectively.

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Adaptive Event-Triggered Control of Time-Varying Nonlinear Systems: A Tight and Powerful Strategy

doi: 10.1109/JAS.2025.125786

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