Adaptive Uniform Performance Control of Strict-Feedback Nonlinear Systems With Time-Varying Control Gain

Kai Zhao; Changyun Wen; Yongduan Song; Frank L. Lewis

doi:10.1109/JAS.2022.106064

Volume 10 Issue 2

Feb. 2023

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2023 > 10(2): 451-461

K. Zhao, C. Y. Wen, Y. D. Song, and F. L. Lewis, “Adaptive uniform performance control of strict-feedback nonlinear systems with time-varying control gain,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 2, pp. 451–461, Feb. 2023. doi: 10.1109/JAS.2022.106064

Citation:

K. Zhao, C. Y. Wen, Y. D. Song, and F. L. Lewis, “Adaptive uniform performance control of strict-feedback nonlinear systems with time-varying control gain,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 2, pp. 451–461, Feb. 2023. doi: 10.1109/JAS.2022.106064

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Adaptive Uniform Performance Control of Strict-Feedback Nonlinear Systems With Time-Varying Control Gain

doi: 10.1109/JAS.2022.106064

1.
Department of Electrical and Computer Engineering, National University of Singapore, Singapore 119077, Singapore
2.
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore
3.
State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing Key Laboratory of Intelligent Unmanned Systems, School of Automation, Chongqing University, Chongqing 400044, China
4.
UTA Research Institute, University of Texas at Arlington, Fort Worth, TX 76118 USA

Funds: This work was supported in part by the National Key Research and Development Program of China (2021ZD0201300) and in part by the National Natural Science Foundation of China (61860206008, 61933012)

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Author Bio:
Kai Zhao (Member, IEEE) received the Ph.D. degree in control theory and control engineering from Chongqing University in 2019. From September 2017 to September 2018, he was a Visiting Ph.D. Student with the School of Electrical Engineering and Computing, The University of Newcastle, Australia. He also held a Postdoctoral Fellow position with the Department of Computer and Information Science, University of Macau, China, from October 2019 to October 2021. Currently he is a Research Fellow with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore. His research interests include adaptive control, prescribed performance control, and robotic control

Changyun Wen (Fellow, IEEE) received the B.Eng. degree from Xi’an Jiaotong University in 1983, and the Ph.D. degree from the University of Newcastle, Australia in 1990. From August 1989 to August 1991, he was a Postdoctoral Fellow at University of Adelaide, Australia. Since August 1991, he has been with Nanyang Technological University, Singapore, where he is currently a Full Professor. His main research activities are in the areas of control systems and applications, cyber-physical systems, smart grids, complex systems and networks. Prof. Wen is a Fellow of IEEE and Fellow of the Academy of Engineering, Singapore. He was a Member of IEEE Fellow Committee from January 2011 to December 2013 and a Distinguished Lecturer of IEEE Control Systems Society from 2010 to 2013. He is currently the co-Editor-in-Chief of IEEE Transactions on Industrial Electronics, Associate Editor of Automatica (from Feb 2006) and Executive Editor-in-Chief of Journal of Control and Decision. He also served as an Associate Editor of IEEE Transactions on Automatic Control from 2000 to 2002, IEEE Transactions on Industrial Electronics from 2013 to 2020 and IEEE Control Systems Magazine from 2009 to 2019. He has been actively involved in organizing international conferences playing the roles of General Chair (including the General Chair of IECON 2020 and IECON 2023), TPC Chair (e.g., the TPC Chair of Chinese Control and Decision Conference since 2008), etc. He was the recipient of a number of awards, including the Prestigious Engineering Achievement Award from the Institution of Engineers, Singapore in 2005, and the Best Paper Award of IEEE Transactions on Industrial Electronics in 2017

Yongduan Song (Fellow, IEEE) received the Ph.D. degree in electrical and computer engineering from Tennessee Technological University, USA, in 1992. He held a tenured Full Professor with North Carolina A&T State University, USA, from 1993 to 2008 and a Langley Distinguished Professor with the National Institute of Aerospace, USA, from 2005 to 2008. He is currently the Chair Professor with School of Automation, Chongqing University. He was one of the six Langley Distinguished Professors with the National Institute of Aerospace (NIA), USA, and the Founding Director of Cooperative Systems with NIA. His current research interests include intelligent systems, guidance navigation and control, and bio-inspired adaptive and cooperative systems. He has served/been serving as an Associate Editor for several prestigious international journals, including the IEEE Transactions on Automatic Control, IEEE Transactions on Neural Networks and Learning Systems, IEEE Transactions on Intelligent Transportation Systems, IEEE Transactions on Systems, Man and Cybernetics, etc. He is currently the Editor-in-Chief for the IEEE Transactions on Neural Networks and Learning Systems

Frank L. Lewis (Life Fellow, IEEE) received the bachelor degree in physics/EE and the M.S.E.E. degree from Rice University, the M.S. degree in aeronautical engineering from the University of Florida, and the Ph.D. degree from Georgia Tech. He is a UTA Charter Distinguished Scholar Professor, a UTA Distinguished Teaching Professor, and the Moncrief-O'Donnell Chair at the University of Texas at Arlington Research Institute. He ranked at position 88 worldwide, 66 in the USA, and three in Texas of all scientists in computer science and electronics, by Guide2Research.com. He has 80 000 Google Scholar Citations. He works in feedback control, intelligent systems, reinforcement learning, cooperative control systems, and nonlinear systems. He is the author of seven U.S. patents, numerous journal special issues, 445 journal articles, 20 books, including the textbooks Optimal Control, Aircraft Control, Optimal Estimation, and Robot Manipulator Control. He is a Fellow of the National Academy of Inventors, IFAC, AAAS, the U.K. Institute of Measurement and Control, and PE Texas; and U.K. Chartered Engineer. He received the Fulbright Research Award, the NSF Research Initiation Grant, the ASEE Terman Award, the International Neural Network Society Gabor Award, the U.K. Inst Measurement and Control Honeywell Field Engineering Medal, the IEEE Computational Intelligence Society Neural Networks Pioneer Award, the AIAA Intelligent Systems Award, and the AACC Ragazzini Award. He has received over fanxiexian_myfh12M in 100 research grants from NSF, ARO, ONR, AFOSR, DARPA, and USA industry contracts. He won the U.S. SBA Tibbets Award in 1996 as the Director of the UTA Research Institute SBIR Program
Corresponding author: Yongduan Song, e-mail: ydsong@cqu.edu.cn
¹ \begin{document}$ {\mathbb{R}} $\end{document} denotes the set of real numbers, \begin{document}${\mathbb{R}}_+ $\end{document} is the set of positive real numbers, and \begin{document}$ {\mathbb{R}}^n $\end{document} represents the set of \begin{document}$ n- $\end{document}dimensional real vectors. Let \begin{document}$ |\bullet| $\end{document} be the absolute value of a real number \begin{document}$ \bullet $\end{document}.
Received Date: 2022-03-18
Revised Date: 2022-05-20
Accepted Date: 2022-06-21

Available Online: 2022-11-04

Abstract

Abstract

In this paper, we present a novel adaptive performance control approach for strict-feedback nonparametric systems with unknown time-varying control coefficients, which mainly includes the following steps. Firstly, by introducing several key transformation functions and selecting the initial value of the time-varying scaling function, the symmetric prescribed performance with global and semi-global properties can be handled uniformly, without the need for control re-design. Secondly, to handle the problem of unknown time-varying control coefficient with an unknown sign, we propose an enhanced Nussbaum function (ENF) bearing some unique properties and characteristics, with which the complex stability analysis based on specific Nussbaum functions as commonly used is no longer required. Thirdly, by utilizing the core-function information technique, the nonparametric uncertainties in the system are gracefully handled so that no approximator is required. Furthermore, simulation results verify the effectiveness and benefits of the approach.
- Adaptive control,
- enhanced Nussbaum function (ENF),
- strict-feedback systems,
- unified prescribed performance

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¹ $ {\mathbb{R}} $ denotes the set of real numbers, ${\mathbb{R}}_+ $ is the set of positive real numbers, and $ {\mathbb{R}}^n $ represents the set of $ n- $dimensional real vectors. Let $ |\bullet| $ be the absolute value of a real number $ \bullet $.

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Different from the PPB-based controls [11], [12], [19], [21], [22], by constructing a unified function and a unique scaling function, the proposed control is flexible to handle the global or symmetric semi-global performance cases uniformly just by selecting the initial value of the time-varying scaling function properly, making the controller re-design and stability re-analysis not required
Different from the specific form of Nussbaum functions in the existing literature [9], [10], [11], [12], in this paper, by defining an enhanced Nussbaum function (ENF) and imposing a condition on the update law of Nussbaum argument, the developed control relaxes the complicated calculation and proof in the existing results
By extracting the core function information from the non- parametric uncertainty, no approximator (such as neural networks and fuzzy logic systems) is required, despite unknown control directions

Adaptive Uniform Performance Control of Strict-Feedback Nonlinear Systems With Time-Varying Control Gain

doi: 10.1109/JAS.2022.106064

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