Fixed-Time Lyapunov Criteria and State-Feedback Controller Design for Stochastic Nonlinear Systems

Huifang Min; Shengyuan Xu; Baoyong Zhang; Qian Ma; Deming Yuan

doi:10.1109/JAS.2022.105539

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): 1005-1014

H. F. Min, S. Y. Xu, B. Y. Zhang, Q. Ma, and D. M. Yuan, “Fixed-time Lyapunov criteria and state-feedback controller design for stochastic nonlinear systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 6, pp. 1005–1014, Jun. 2022. doi: 10.1109/JAS.2022.105539

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H. F. Min, S. Y. Xu, B. Y. Zhang, Q. Ma, and D. M. Yuan, “Fixed-time Lyapunov criteria and state-feedback controller design for stochastic nonlinear systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 6, pp. 1005–1014, Jun. 2022. doi: 10.1109/JAS.2022.105539

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Fixed-Time Lyapunov Criteria and State-Feedback Controller Design for Stochastic Nonlinear Systems

doi: 10.1109/JAS.2022.105539

Huifang Min^1
,,
Shengyuan Xu^{1
,
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Baoyong Zhang^1
,,
Qian Ma^1
,,
Deming Yuan^1
,

School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China

Funds: This work was supported in part by the National Natural Science Foundation of China (62073166, 61673215), and the Key Laboratory of Jiangsu Province

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Author Bio:
Huifang Min received the B.Sc. degree from the Zhejiang Ocean University in 2012, M.Sc. degree from Jiangsu Normal University in 2015, and Ph.D. degree from the Nanjing University of Science and Technology in 2019. From July 2019 to June 2021, She was a Postdoctoral Researcher in the School of Automation at Southeast University. Since June 2021, she has joined the School of Automation at Nanjing University of Science and Technology as a Young Professor. Her research interests include nonlinear adaptive control and stochastic nonlinear control

Shengyuan Xu received the B.Sc. degree from the Hangzhou Normal University in 1990, M.Sc. degree from the Qufu Normal University in 1996, and Ph.D. degree from the Nanjing University of Science and Technology in 1999. From 1999 to 2000, he was a Research Associate in the Department of Mechanical Engineering at the University of Hong Kong, Hong Kong, China. From December 2000 to November 2001, and December 2001 to September 2002, he was a Postdoctoral Researcher in CESAME at the Universite catholique de Louvain, Belgium, and the Department of Electrical and Computer Engineering at the University of Alberta, Canada, respectively. Since November 2002, he has joined the School of Automation at the Nanjing University of Science and Technology as a Professor. Dr. Xu was a Recipient of the National Excellent Doctoral Dissertation Award in the year 2002 from the Ministry of Education of China. He obtained a grant from the National Science Foundation for Distinguished Young Scholars of China in the year 2006. He was awarded a Cheung Kong Professorship in the year 2008 from the Ministry of Education of China.Dr. Xu is a Member of the Editorial Boards of the Transactions of the Institute of Measurement and Control, and the Journal of the Franklin Institute. His current research interests include robust filtering and control, singular systems, time-delay systems, neural networks, multidimensional systems and nonlinear systems

Baoyong Zhang received the B.Sc. degree and M.Sc. degree from Qufu Normal University in 2003 and 2006, respectively, and Ph.D. degree from Nanjing University of Science and Technology (NJUST) in 2011. From March 2008 to June 2008, he was a Research Associate in the Department of Mechanical Engineering, the University of Hong Kong, Hong Kong, China. From November 2008 to July 2009, he was a Visiting Fellow at the School of Computing and Mathematics, the University of Western Sydney, Australia. From December 2011 to December 2012, he was a Postdoctoral Fellow in the Department of Mechanical Engineering, the University of Hong Kong, Hong Kong, China. He joined the School of Automation at NJUST as Lecturer in November 2010 and was selected as Young Professor of NJUST in August 2014. His research interests include robust control and filtering, time-delay systems, stochastic systems, switched systems, nonlinear systems, LPV systems and complex networks

Qian Ma received the B.S. from Jiangsu University of Science and Technology in 2005, M.S. and Ph.D. from Nanjing University of Science and Technology, in 2007 and 2013. Since June 2013, she has joined the School of Automation at Nanjing University of Science and Technology, where she is currently a Professor. Her current research interests include time-delay systems, stability theory, and cooperative control

Deming Yuan received the B.Sc. degree in electrical engineering and automation and the Ph.D. degree in control science and engineering from the Nanjing University of Science and Technology in 2007 and 2012, respectively. He is currently a Professor with the School of Automation, Nanjing University of Science and Technology. He received the Australia Award Endeavour Research Fellowship to further his research on distributed optimization, and was hosted by the Australian National University, in 2018. He has been on the editorial board of Transactions of the Institute of Measurement and Control. His current research interests include algorithms for distributed optimization, control, and machine learning
Corresponding author: Shengyuan Xu, e-mail: syxu@njust.edu.cn
Received Date: 2021-11-27
Accepted Date: 2022-01-04

Available Online: 2022-03-07

Abstract

Abstract

This paper investigates the fixed-time stability theorem and state-feedback controller design for stochastic nonlinear systems. We propose an improved fixed-time Lyapunov theorem with a more rigorous and reasonable proof procedure. In particular, an important corollary is obtained, which can give a less conservative upper-bound estimate of the settling time. Based on the backstepping technique and the addition of a power integrator method, a state-feedback controller is skillfully designed for a class of stochastic nonlinear systems. It is proved that the proposed controller can render the closed-loop system fixed-time stable in probability with the help of the proposed fixed-time stability criteria. Finally, the effectiveness of the proposed controller is demonstrated by simulation examples and comparisons.
- Fixed-time stability,
- Lyapunov theorem,
- state-feedback control,
- stochastic nonlinear systems

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References(47)

References

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An improved fixed-time Lyapunov theorem with a more rigorous and reasonable proof procedure is proposed
A less conservative upper-bound estimate of the settling time is proved and obtained
A state-feedback controller is constructed by using backstepping, the adding a power integrator method and the fixed-time control procedure
The property of fixed-time stability in probability is obtained

Fixed-Time Lyapunov Criteria and State-Feedback Controller Design for Stochastic Nonlinear Systems

doi: 10.1109/JAS.2022.105539

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通讯作者: 陈斌, bchen63@163.com

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