Fault-tolerant control for uncertain linear systems via adaptive and LMI approaches

ABSTRACT

This paper proposes a fault-tolerant control scheme for linear systems with mismatched uncertainties which are assumed to be norm-bounded, affine and polytopic, respectively. The linear fractional transformation (LFT) and linear matrix inequality (LMI) techniques are introduced to handle the mismatched uncertainties, and the adaptive techniques are used to compensate actuator faults. By using the cone complementary linearisation algorithm, the resulting stability criteria are converted into solvable ones. Then, on the basis of Lyapunov stability theory, it is shown that the solutions to the closed-loop system and error system are uniformly bounded, especially, the states converge asymptotically to zero. Finally, simulations are given to illustrate the effectiveness and advantages of the proposed theoretical results.

KEYWORDS:

• Adaptive fault-tolerant control
• LFT
• LMI
• robust control
• mismatched uncertainties

Acknowledgments

The authors would like to thank the associate editor and the anonymous reviewers for their detailed comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the Funds of National Science of China [grant number 61273148], 61420106016, 61403070); the Fundamental Research Funds for the Central Universities [grant number N140402002], [grant number N150404025]; China Postdoctoral Science Foundation Special Funded Project [grant number 2015T80263]; and The Research Fund of State Key Laboratory of Synthetical Automation for Process Industries [grant number 2013ZCX01].

Notes on contributors

Yan Liu

Yan Liu received her B.S. degree in automation from Qufu Normal University, Rizhao, China, in 2014. She is studying for the M.S. degree in Control Theory and Control Engineering in Northeastern University, Shenyang, China. Her research interests include fault diagnosis, fault-tolerant control.

Guang-Hong Yang

Guang-Hong Yang received his B.S. and M.S. degrees from Northeast University of Technology, Liaoning, China, in 1983 and 1986, respectively, and his Ph.D. degree in Control Engineering from Northeastern University, China (formerly, Northeast University of Technology), in 1994. He was a Lecturer/Associate Professor with Northeastern University from 1986 to 1995. He joined the Nanyang Technological University in 1996 as a Postdoctoral Fellow. From 2001 to 2005, he was a Research Scientist/Senior Research Scientist with the National University of Singapore. He is currently a Professor at the College of Information Science and Engineering, Northeastern University. His current research interests include fault-tolerant control, fault detection and isolation, non-fragile control systems design, and robust control. Dr Yang is an Associate Editor for the International Journal of Control, Automation, and Systems (IJCAS), the International Journal of Systems Science (IJSS), the IET Control Theory & Applications, and the IEEE Transactions on Fuzzy Systems.

Xiao-Jian Li

Xiao-Jian Li received his B.S. and M.S. degrees in mathematics from Northeast Normal University, China, in 2003 and 2006, respectively, and his Ph.D. degree in Control Theory and Engineering from Northeastern University, China, in 2011. He is currently an associate professor at the College of Information Science and Engineering, Northeastern University. His research interests include fault diagnosis, fault-tolerant control, fuzzy control, and complex networks.