Fixed-Time Stabilization of a Class of Strict-Feedback Nonlinear Systems via Dynamic Gain Feedback Control

Chenghui Zhang; Le Chang; Lantao Xing; Xianfu Zhang

doi:10.1109/JAS.2023.123408

Volume 10 Issue 2

Feb. 2023

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 15.3, Top 1 (SCI Q1)

CiteScore: 23.5, Top 2% (Q1)
Google Scholar h5-index: 77， TOP 5

Turn off MathJax

Article Contents

Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2023 > 10(2): 403-410

C. H. Zhang, L. Chang, L. T. Xing, and X. F. Zhang, “Fixed-time stabilization of a class of strict-feedback nonlinear systems via dynamic gain feedback control,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 2, pp. 403–410, Feb. 2023. doi: 10.1109/JAS.2023.123408

Citation:

C. H. Zhang, L. Chang, L. T. Xing, and X. F. Zhang, “Fixed-time stabilization of a class of strict-feedback nonlinear systems via dynamic gain feedback control,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 2, pp. 403–410, Feb. 2023. doi: 10.1109/JAS.2023.123408

Citation:

PDF( 935 KB)

Fixed-Time Stabilization of a Class of Strict-Feedback Nonlinear Systems via Dynamic Gain Feedback Control

doi: 10.1109/JAS.2023.123408

1.
School of Control Science and Engineering, Shandong University, Jinan 250012, China
2.
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China

Funds: This work was supported by the National Natural Science Foundation of China (61821004, U1964207, 20221017-10)

More Information

Author Bio:
Chenghui Zhang (Fellow, IEEE) received the bachelor and master degrees in automation engineering from Shandong University of Technology, in 1985 and 1988, respectively, and the Ph.D. degree in control theory and operational research from Shandong University, in 2001, respectively. He is currently a Professor and the Dean of the School of Control Science and Engineering, Shandong University. He has also served as the Chief Manager of Power Electronic Energy-saving Technology and Equipment Research Center, a Changjiang-Scholar Professor by China Ministry of Education, and a Taishan Scholar Climbing Plan Expert. He is also the Academic Leader of Creative Research Groups of China, the Leader of Innovation Team of Ministry of Education, and the Chief Expert of the National “863” High Technological Planning. His research interests include optimal control of engineering, power electronics and motor drives, energy-saving techniques, and networked control systems

Le Chang (Member, IEEE) received the B.S. degree in mathematics, and the Ph.D. degree in control science and engineering from Shandong University in 2012 and 2020, respectively. From 2017 to 2019, he was a visiting Ph.D. student with the Swinburne University of Technology, Australia. Since 2020, he has been as a Postdoctoral Researcher at Shanghai Jiao Tong University. His research interests include distributed estimation and control of nonlinear systems

Lantao Xing (Member, IEEE) received the Ph.D. degree in control science and engineering from Zhejiang University, in 2018. Then, he worked respectively as a Research Fellow and a Presidential Postdoctoral Fellow at Queensland University of Technology, Australia, and Nanyang Technological University, Singapore. Currently, he is a Full Professor with the School of Control Science and Engineering, Shandong University. His research interests include nonlinear system control, event-triggered control, and distributed control with applications in smart grid

Xianfu Zhang (Member, IEEE) received the M.Sc. degree in mathematics from the School of Mathematics Sciences, Shandong Normal University, in 1999, and the Ph.D. degree in operational research and control from the School of Mathematics, Shandong University, in 2005. From 1999 to 2011, he worked in the School of Science, Shandong Jianzhu University. He joined the School of Control Science and Engineering, Shandong University, in 2012, where he is currently a Professor. From September 2008 to February 2009, he was a Visiting Scholar in the Department of Mechanical Engineering, Ecole Polytechnique de Montreal, Canada. From November 2009 to February 2010, and from July 2012 to October 2012, he was a Research Assistant in City University of Hong Kong, Hong Kong, China. His main research interests include nonlinear systems, fractional-order systems, and time-delay systems. He received the Prize of Shandong Natural Science in 2017, and he was recognized as the Taishan Scholar Distinguished Professor of Shandong Province in 2019
Corresponding author: Chenghui Zhang, e-mail: zchui@sdu.edu.cn
Received Date: 2022-11-14
Accepted Date: 2022-12-26

Available Online: 2023-04-12

Abstract

Abstract

This paper presents a novel fixed-time stabilization control (FSC) method for a class of strict-feedback nonlinear systems involving unmodelled system dynamics. The key feature of the proposed method is the design of two dynamic parameters. Specifically, a set of auxiliary variables is first introduced through state transformation. These variables combine the original system states and the two introduced dynamic parameters, facilitating the closed-loop system stability analyses. Then, the two dynamic parameters are delicately designed by utilizing the Lyapunov method, ensuring that all the closed-loop system states are globally fixed-time stable. Compared with existing results, the “explosion of complexity” problem of backstepping control is avoided. Moreover, the two designed dynamic parameters are dependent on system states rather than a time-varying function, thus the proposed controller is still valid beyond the given fixed-time convergence instant. The effectiveness of the proposed method is demonstrated through two practical systems.
- Dynamic gain feedback control,
- fixed-time stabilization,
- strict-feedback nonlinear system

FullText(HTML)

References(34)

References

[1]	Y. Liu, H. Li, Z. Zuo, X. Li, and R. Lu, “An overview of finite/fixed-time control and its application in engineering systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 12, pp. 2106–2120, 2022.
[2]	A. Polyakov, “Nonlinear feedback design for fixed-time stabilization of linear control systems,” IEEE Trans. Automat. Control, vol. 57, no. 8, pp. 2106–2110, Aug. 2012. doi: 10.1109/TAC.2011.2179869
[3]	F. L. Chernousko, I. M. Ananievski, and S. A. Reshmin, “Control of nonlinear dynamical systems: Methods and applications,” Springer Science & Business Media, 2008.
[4]	M. Defoort, A. Polyakov, G. Demesure, M. Djemai, and K. Veluvolu, “Leader-follower fixed-time consensus for multi-agent systems with unknown non-linear inherent dynamics,” IET Control Theory Appli., vol. 9, no. 14, pp. 2165–2170, Sep. 2015. doi: 10.1049/iet-cta.2014.1301
[5]	H. Hong, W. Yu, G. Wen, and X. Yu, “Distributed robust fixed-time consensus for nonlinear and disturbed multiagent systems,” IEEE Trans. Syst. Man,Cybern. Syst., vol. 47, no. 7, pp. 1464–1473, Jul. 2016.
[6]	B. Ning and Q.-L. Han, “Prescribed finite-time consensus tracking for multiagent systems with nonholonomic chained-form dynamics,” IEEE Trans. Automat. Control, vol. 64, no. 4, pp. 1686–1693, Apr. 2019. doi: 10.1109/TAC.2018.2852605
[7]	L. Zhang, Y. Xia, G. Shen, and B. Cui, “Fixed-time attitude tracking control for spacecraft based on a fixed-time extended state observer,” Sci. China Inform. Sci., vol. 64, no. 11, pp. 212201:1–212201:17, Oct. 2021.
[8]	B. Ning, Q.-L. Han, and Z. Zuo, “Practical fixed-time consensus for integrator-type multi-agent systems: A time base generator approach,” Automatica, vol. 105, pp. 406–414, Jul. 2019. doi: 10.1016/j.automatica.2019.04.013
[9]	Y. Song, Y. Wang, J. Holloway, and M. Krstic, “Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time,” Automatica, vol. 83, pp. 243–251, Sep. 2017. doi: 10.1016/j.automatica.2017.06.008
[10]	L. Chang, Q.-L. Han, X. Ge, C. Zhang, and X. Zhang, “On designing distributed prescribed finite-time observers for strict-feedback nonlinear systems,” IEEE Trans. Cyber., vol. 51, no. 9, pp. 4695–4706, Sep. 2021. doi: 10.1109/TCYB.2019.2951067
[11]	Y. Wang, Y. Song, D. J. Hill, and M. Krstic, “Prescribed-time consensus and containment control of networked multiagent systems,” IEEE Trans. Cyber., vol. 49, no. 4, pp. 1138–1147, Apr. 2019. doi: 10.1109/TCYB.2017.2788874
[12]	J. Li, Y. Yang, C. Hua, and X. Guan, “Fixed-time backstepping control design for high-order strict-feedback non-linear systems via terminal sliding mode,” IET Control Theory Appli., vol. 11, no. 8, pp. 1184–1193, Sep. 2016.
[13]	C. Hua, Y. Li, and X. Guan, “Finite/fixed-time stabilization for nonlinear interconnected systems with dead-zone input,” IEEE Trans. Automat. Control, vol. 62, no. 5, pp. 2554–2560, May 2017. doi: 10.1109/TAC.2016.2600343
[14]	F. Lopez-Ramirez, A. Polyakov, D. Efimov, and W. Perruquetti, “Finite-time and fixed-time observer design: Implicit Lyapunov function approach,” Automatica, vol. 87, pp. 52–60, Feb. 2018. doi: 10.1016/j.automatica.2017.09.007
[15]	Y. Sun, F. Wang, Z. Liu, Y. Zhang, and C. L. Chen, “Fixed-time fuzzy control for a class of nonlinear systems,” IEEE Trans. Cyber., vol. 52, no. 5, pp. 3880–3887, May 2022. doi: 10.1109/TCYB.2020.3018695
[16]	B. Zhou, W. Michiels, and J. Chen, “Fixed-time stabilization of linear delay systems by smooth periodic delayed feedback,” IEEE Trans. Automat. Control, vol. 67, no. 2, pp. 557–573, Feb. 2022. doi: 10.1109/TAC.2021.3051262
[17]	L. Praly, “Asymptotic stabilization via output feedback for lower triangular systems with output dependent incremental rate,” IEEE Trans. Automat. Control, vol. 48, no. 6, pp. 1103–1108, Jun. 2003. doi: 10.1109/TAC.2003.812819
[18]	L. Praly and Z. Jiang, “Linear output feedback with dynamic high gain for nonlinear systems,” Syst. Control Letters, vol. 53, no. 2, pp. 107–116, Oct. 2004. doi: 10.1016/j.sysconle.2004.02.025
[19]	Q. Liu and Z. Liang, “Finite-time consensus of time-varying nonlinear multi-agent systems,” Int. J. Syst. Sci., vol. 47, no. 11, pp. 2642–2651, Aug. 2016. doi: 10.1080/00207721.2015.1010190
[20]	X. Zhang, G. Feng, and Y. Sun, “Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems,” Automatica, vol. 48, no. 3, pp. 499–504, Mar. 2012. doi: 10.1016/j.automatica.2011.07.014
[21]	D. Fan, X. Zhang, Y. Chang, and X. Lu, “Global practical tracking via disturbance rejection control for uncertain nonlinear systems with quantized input and output,” Sci. China Inform. Sci., vol. 65, pp. 119201:1–119201:3, Feb. 2021.
[22]	M. S. Koo, H. L. Choi, and J. T. Lim, “Global regulation of a class of uncertain nonlinear systems by switching adaptive controller,” IEEE Trans. Autom. Control, vol. 55, no. 12, pp. 2822–2827, Dec. 2010. doi: 10.1109/TAC.2010.2069430
[23]	H. L. Choi and J. T. Lim, “Stabilization of a class of nonlinear systems by adaptive output feedback,” Automatica, vol. 41, no. 6, pp. 1091–1097, Jun. 2005. doi: 10.1016/j.automatica.2005.01.009
[24]	C. Qian and W. Lin, “Output feedback control of a class of nonlinear systems: A nonseparation principle paradigm,” IEEE Trans. Automat. Control, vol. 47, no. 10, pp. 1710–1715, Oct. 2002. doi: 10.1109/TAC.2002.803542
[25]	W. Wang, J. Long, J. Zhou, J. Huang, and C. Y. Wen, “Adaptive backstepping based consensus tracking of uncertain nonlinear systems with event-triggered communication,” Automatica, vol. 133, pp. 109841:1–109841:9, Aug. 2021.
[26]	W. Chang, Y. Li, and S. Tong, “Adaptive fuzzy backstepping tracking control for flexible robotic manipulator,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 12, pp. 1923–1930, Dec. 2021. doi: 10.1109/JAS.2017.7510886
[27]	Z. Gao and G. Guo, “Command filtered finite/fixed-time heading tracking control of surface vehicles,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 10, pp. 1667–1776, Oct. 2021. doi: 10.1109/JAS.2021.1004135
[28]	J. Liu, Y. Wu, M. Sun, and C. Sun, “Fixed-time cooperative tracking for delayed disturbed multi-agent systems under dynamic event-triggered control,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 5, pp. 930–933, May 2022. doi: 10.1109/JAS.2022.105503
[29]	F. Wang and G. Lai, “Fixed-time control design for nonlinear uncertain systems via adaptive method,” Syst. Control Letters, vol. 140, pp. 104704:1–104740:7, Jun. 2020.
[30]	S. Bhat and S. D. Bernstein, “Finite-time stability of continuous autonomous systems,” SIAM J. Control Optim., vol. 38, no. 3, pp. 751–766, Oct. 2000. doi: 10.1137/S0363012997321358
[31]	C. Qian and W. Lin, “Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization,” Syst. Control Letters, vol. 42, no. 3, pp. 185–200, Mar. 2001. doi: 10.1016/S0167-6911(00)00089-X
[32]	P. Krishnamurthy and F. Khorrami, “On uniform solvability of parameter-dependent Lyapunov inequalities and applications to various problems,” SIAM J. Control Optim., vol. 45, no. 4, pp. 1147–1164, Sep. 2006. doi: 10.1137/040619417
[33]	W. Li, X. Yao, and M. Krstic, “Adaptive-gain observer-based stabilization of stochastic strict-feedback systems with sensor uncertainty,” Automatica, vol. 120, pp. 109112:1–109112:12, Jul. 2020.
[34]	Z.-L. Zhao and Z.-P. Jiang, “Semi-global finite-time output-feedback stabilization with an application to robotics,” IEEE Trans. Ind. Electron., vol. 66, no. 4, pp. 3148–3156, Apr. 2019. doi: 10.1109/TIE.2018.2847630

Supplements(0)

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(2) / Tables(1)

Get Citation

PDF

XML

Article Metrics

Article views (485) PDF downloads(122)

Highlights

This paper presents a novel fixed-time stabilization control method for a class of strict-feedback nonlinear systems involving unmodelled system dynamics. The key feature of the proposed method is the design of two dynamic parameters, facilitating the closed-loop system stability analyses
The two dynamic parameters are delicately designed by utilizing the Lyapunov method, ensuring that all the closed-loop system states are globally fixed-time stable. Compared with existing results, the ``explosion of complexity" problem of backstepping control is avoided
Moreover, the two designed dynamic parameters are dependent on system states rather than a time-varying function, thus the proposed controller is still valid beyond the given fixed-time convergence instant. The effectiveness of the proposed method is demonstrated through two practical systems

Fixed-Time Stabilization of a Class of Strict-Feedback Nonlinear Systems via Dynamic Gain Feedback Control

doi: 10.1109/JAS.2023.123408

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Highlights

Export File

Citation

Format

Content