Adaptive Control With Guaranteed Transient Behavior and Zero Steady-State Error for Systems With Time-Varying Parameters

Hefu Ye; Yongduan Song

doi:10.1109/JAS.2022.105608

Volume 9 Issue 6

Jun. 2022

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2022 > 9(6): 1073-1082

H. F. Ye and Y. D. Song, “Adaptive control with guaranteed transient behavior and zero steady-state error for systems with time-varying parameters,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 6, pp. 1073–1082, Jun. 2022. doi: 10.1109/JAS.2022.105608

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H. F. Ye and Y. D. Song, “Adaptive control with guaranteed transient behavior and zero steady-state error for systems with time-varying parameters,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 6, pp. 1073–1082, Jun. 2022. doi: 10.1109/JAS.2022.105608

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Adaptive Control With Guaranteed Transient Behavior and Zero Steady-State Error for Systems With Time-Varying Parameters

doi: 10.1109/JAS.2022.105608

Hefu Ye^{1, 2
,},
Yongduan Song^{1
,
,}

1.
Chongqing Key Laboratory of Autonomous Systems, Institute of Artificial Intelligence, School of Automation, Chongqing Univer-sity, Chongqing 400044, China
2.
Star Institute of Intelligent Systems (SIIS), Chongqing 400044, China

Funds: This work was supported by the National Natural Science Foundation of China (61991400, 61991403, 61860206008, 61933012)

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Author Bio:
Hefu Ye received the B.Eng. degree at the School of Information Science and Engineering in 2019 from Harbin Institute of Technology. He is currently pursuing the Ph.D. degree with the School of Automation, Chongqing University. His research interests include multi-agent systems, robotic systems, robust adaptive control, prescribed performance control, and prescribed-time control. He is an active Reviewer for many international journals, including the IEEE Transactions on Automatic Control, IEEE Transactions on Systems, Man, and Cybernetics: Systems, IEEE Transactions on Neural Networks and Learning Systems, etc

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 Dean of the 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 CooperativeSystems with NIA. His current research interests include intelligent systems, guidance navigation and control, and bio-inspired adaptive and cooperative systems. Prof. Song was a recipient of several competitive research awards from the National Science Foundation, the National Aeronautics and Space Administration, the U.S. Air Force Office, the U.S. Army Research Office, and the U.S. Naval Research Office. 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 an Editor-in-Chief for the IEEE Transactions on Neural Networks and Learning Systems
Corresponding author: Yongduan Song, e-mail: ydsong@cqu.edu.cn
¹ Properties 1 and 2 of \begin{document}$ \psi(x) $\end{document} ensure that \begin{document}$ \psi_x $\end{document} is positive and invertible for all \begin{document}$ x \in \mathbb{R} $\end{document}.
² For simplicity, arguments of functions are sometimes omitted if no confusion occurs.
³ Note that when \begin{document}$ \theta(t) $\end{document} is an unknown constant and \begin{document}$ b(t)=1 $\end{document}, this model is a simplified version of the one studied by [37], where the exponential regulation is proposed for a class of strict-feedback systems with known control gain and unknown constants θ.⁴ Here \begin{document}$ b(t) $\end{document} and \begin{document}$ \theta(t) $\end{document} are fast time-varying parameters and they are only piecewise continuous yet \begin{document}$ b(t) $\end{document} may undergo sudden changes. Therefore, some classical adaptive schemes [15], [19] are not available because those methods require the parameters be slow time-varying (i.e., here exists a parameter ϵ such that \begin{document}$ |\dot{\theta}(t)|<\epsilon $\end{document} and \begin{document}$ |\dot b(t)|<\epsilon $\end{document}).
Received Date: 2021-12-30
Revised Date: 2022-02-17
Accepted Date: 2022-03-02

Available Online: 2022-04-09

Abstract

Abstract

It is nontrivial to achieve global zero-error regulation for uncertain nonlinear systems. The underlying problem becomes even more challenging if mismatched uncertainties and unknown time-varying control gain are involved, yet certain performance specifications are also pursued. In this work, we present an adaptive control method, which, without the persistent excitation (PE) condition, is able to ensure global zero-error regulation with guaranteed output performance for parametric strict-feedback systems involving fast time-varying parameters in the feedback path and input path. The development of our control scheme benefits from generalized ${\boldsymbol{t}}$-dependent and ${\boldsymbol{x}}$-dependent functions, a novel coordinate transformation and “congelation of variables” method. Both theoretical analysis and numerical simulation verify the effectiveness and benefits of the proposed method.
- Adaptive control,
- global property,
- guaranteed performance,
- uncertain nonlinear systems

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¹ Properties 1 and 2 of $ \psi(x) $ ensure that $ \psi_x $ is positive and invertible for all $ x \in \mathbb{R} $.
² For simplicity, arguments of functions are sometimes omitted if no confusion occurs.
³ Note that when $ \theta(t) $ is an unknown constant and $ b(t)=1 $, this model is a simplified version of the one studied by [37], where the exponential regulation is proposed for a class of strict-feedback systems with known control gain and unknown constants θ.⁴ Here $ b(t) $ and $ \theta(t) $ are fast time-varying parameters and they are only piecewise continuous yet $ b(t) $ may undergo sudden changes. Therefore, some classical adaptive schemes [15], [19] are not available because those methods require the parameters be slow time-varying (i.e., here exists a parameter ϵ such that $ |\dot{\theta}(t)|<\epsilon $ and $ |\dot b(t)|<\epsilon $).

References(40)

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This paper provides an adaptive PPC scheme for parameter-varying nonlinear systems
The proposed error transformation is new, resulting in a global solution independent of accurate initial error
Zero-error regulation is achieved for parameter-varying nonlinear systems in the absence of PE condition

Adaptive Control With Guaranteed Transient Behavior and Zero Steady-State Error for Systems With Time-Varying Parameters

doi: 10.1109/JAS.2022.105608

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