A Continuous-Time Framework of Model-Free Adaptive Control for Nonlinear Plants

Hao Yu; Wangjiang Li; Linxin Che; Dawei Shi; Zhongsheng Hou

doi:10.1109/JAS.2025.125789

Volume 13 Issue 4

Apr. 2026

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2026 > 13(4): 966-982

H. Yu, W. Li, L. Che, D. Shi, and Z. Hou, “A continuous-time framework of model-free adaptive control for nonlinear plants,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 4, pp. 966–982, Apr. 2026. doi: 10.1109/JAS.2025.125789

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H. Yu, W. Li, L. Che, D. Shi, and Z. Hou, “A continuous-time framework of model-free adaptive control for nonlinear plants,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 4, pp. 966–982, Apr. 2026. doi: 10.1109/JAS.2025.125789

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A Continuous-Time Framework of Model-Free Adaptive Control for Nonlinear Plants

doi: 10.1109/JAS.2025.125789

Funds: This work was supported by the National Science Foundation of China (62403049, 62373206, 62261160575) and the National Key Research and Development Program of China (2023YFE0204100)

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Author Bio:
Hao Yu (Member, IEEE) received the B.S. and the Ph.D. degrees in control theory and engineering from Beihang University in 2013 and 2018, respectively. From 2019 to 2022, he was a Postdoctoral Fellow in the Department of Electrical and Computer Engineering, at the University of Alberta, Canada. He is presently a Professor at the School of Automation at Beijing Institute of Technology. His research interests include hybrid systems, event-triggered control, multi-agent systems, data-driven PID control, adaptive control, and cyber-physical systems

Wangjiang Li received the B.S. degree in mathematics from Northeast Electric Power University and the M.S. degree in mathematics from China Three Gorges University in 2019 and 2023, respectively. He is currently pursuing the Ph.D. degree in control science and control engineering at Beijing Institute of Technology. His current research interests include model-free adaptive control, network control systems, and multi-agent systems

Linxin Che is currently pursuing the B.Eng. degree at the Automation at Beijing Institute of Technology. Her current research interests include data-driven control, model-free adaptive control, and adaptive control for connected systems

Dawei Shi (Senior Member, IEEE) received the B.Eng. degree in electrical engineering and its automation from the Beijing Institute of Technology in 2008, the Ph.D. degree in control systems from the University of Alberta, Edmonton, Canada, in 2014. In December 2014, he was appointed as an Associate Professor at the School of Automation, Beijing Institute of Technology. From February 2017 to July 2018, he was with the Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, as a Postdoctoral Fellow in bioengineering. Since July 2018, he has been with the School of Automation, Beijing Institute of Technology, where he is a professor. His research focuses on the analysis and synthesis of complex sampled-data control systems with applications to biomedical engineering, robotics, and motion systems. He serves as an Associate Editor/Technical Editor for IEEE Transactions on Industrial Electronics, IEEE/ASME Transactions on Mechatronics, IEEE Control Systems Letters, and IET Control Theory and Applications. He is a member of the Early Career Advisory Board of Control Engineering Practice. He was a Guest Editor for European Journal of Control. He served as an associate editor for IFAC World Congress and is a member of the IEEE Control Systems Society Conference Editorial Board. He is a Senior Member of the IEEE

Zhongsheng Hou (Fellow, IEEE) received the B.S. and M.S. degrees in applied mathematics from the Jilin University of Technology in 1983 and 1988, respectively, and the Ph.D. degree in control theory and applications from Northeastern University in 1994. From 1997 to 2018, he was a Distinguished Professor and the Head of the Department of Automatic Control, Beijing Jiaotong University. He is currently the Chair Professor with the School of Automation, Qingdao University. His research interests are data-driven control, model-free adaptive control, learning control, and intelligent transportation systems. Dr. Hou is also the Founding Director of the Technical Committee on Data-Driven Control, Learning and Optimization, Chinese Association of Automation (CAA). He is a fellow of CAA. He is also an International Federation of Automatic Control Technical Committee Member of Adaptive and Learning Systems and Transportation Systems
Corresponding author: Hao Yu, e-mail: yuhaocsc@bit.edu.cn
¹ In this paper, the term, practical stability, denotes the ultimate boundedness stability defined in Section 4.8 in [30].
Received Date: 2025-04-27
Revised Date: 2025-06-16
Accepted Date: 2025-08-06

Abstract

Abstract

Continuous-time model-free adaptive control frameworks are proposed in this paper for solving tracking problems of unknown nonlinear plants described by high-order differential equations. To tackle situations where no form or structural information of plant models is present, the first step involves introducing continuous-time dynamic linearization techniques to create data models. Based on different ways for generating control inputs, two kinds of dynamic linearization processes for continuous-time nonlinear plants are established for the first time, where the nonlinear plants are parameterized by a time-varying linear data model. In the first dynamic linearization model (DLM), the control input is calculated by designating its derivative while the second one gives directly control inputs. Then, after acquiring different dynamic linearization models, based on traditional backstepping methods, adaptive laws are proposed to learn the time-varying parameters in DLMs and the corresponding model-free adaptive controllers are designed. The conditions on designable parameters for the proposed controllers are provided to ensure semi-global practical stabilization and arbitrarily desirable ultimate tracking accuracy. Moreover, to eliminate the effects of unknown equilibrium points on tracking accuracy, a continuous-time model-free adaptive controller with pure integral terms is proposed under the second dynamic linearization model. Finally, several practical and numerical examples are simulated to illustrate the feasibility and efficiency of the proposed results.
- Backstepping methods,
- continuous-time systems,
- dynamic linearization,
- model-free adaptive control (MFAC),
- nonlinear systems

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¹ In this paper, the term, practical stability, denotes the ultimate boundedness stability defined in Section 4.8 in [30].

References(36)

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A Continuous-Time Framework of Model-Free Adaptive Control for Nonlinear Plants

doi: 10.1109/JAS.2025.125789

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