Robust fast adaptive fault estimation and tolerant control for T-S fuzzy systems with interval time-varying delay

ABSTRACT

This paper studies the problem of fault estimation (FE) and the active fault tolerant control (FTC) for Takagi–Sugeno (T-S) fuzzy systems with interval time-varying delay and norm-bounded external disturbance. Based on the fast adaptive fault estimation (FAFE) algorithm, our attention focuses on designing an adaptive observer-based controller to guarantee the filtering error system to be asymptotically stable and satisfy theH_∞ performance index. By constructing a new Lyapunov–Krasovskii functional including the information of the lower and upper delay bounds, the sufficient delay-dependent conditions have been established to guarantee the existence of adaptive observer-based controller in terms of linear matrix inequalities (LMIs). Compared with the constant delay and time-varying delay, the interval time-varying delay is the less conservative form. Furthermore, we make full use of the information of the delay and no terms are ignored when the stability of the system is analysed. In addition, the results for the systems with time-varying structured uncertainties are established. The results of the active FTC are showed in terms of LMIs. Finally, two examples are given to verify the effectiveness of the proposed method.

KEYWORDS:

• Fast adaptive fault estimation
• linear matrix inequality
• active fault tolerant control
• interval time-varying delay
• delay dependence

Acknowledgments

The authors would like to thank the AE and reviewers for their careful reading, constructive comments and fruitful suggestions that certainly improved the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61304219]; National Natural Science Foundation of China [grant number 61533007; the State Key Laboratory of Synthetical Automation for Process Industries Fundamental Research Funds [grant number 2013ZCX02-04].

Notes on contributors

Hui Li

Hui Li was born in 1990. She received her BS degree from Shenyang University of Technology in 2013. She received her MS degree from Northeastern University in 2015. She is currently a PhD candidate with the Department of Automation in Northeastern University. Her main research interests include fault diagnosis and FTC for nonlinear systems.

Fuqiang You

Fuqiang You was born in 1978. He received the BS and MS degrees from Harbin Institute of Technology, Harbin, China, in 2000 and 2002, respectively. He received the PhD degree from Shanghai Jiaotong University, Shanghai, China, in 2005. He is an associate professor of School of Information Science and Engineering in Northeastern University, Shenyang, China. His primary research interests include fault diagnosis of time-delay systems and H_∞filtering.

Fuli Wang

Fuli Wang was born in 1957. He received his PhD degree from Northeastern University in 1987. He is a professor and adviser of School of Information Science and Engineering in Northeastern University, Shenyang, China. His research interests include control application and new remote monitoring and control.

Shouping Guan

Shouping Guan received his PhD degree in automatic control from Northeastern University in 1995. He is currently a professor in Northeastern University, and his research interests are in process optimal control, intelligent control, monitoring and diagnosis in biochemical process, and other batch-like industrial control applications.