Non-fragile sliding mode observer based fault estimation for interval type-2 fuzzy singular fractional order systems

Abstract

In this paper, an interval type-2 fuzzy model is presented to describe the nonlinear singular fractional order systems (SFOSs) with $0<\alpha <2$. The problem of actuator and sensor fault estimation is addressed by designing a non-fragile sliding mode observer (SMO). Firstly, a new criterion is provided to analyse the admissibility of SFOSs, which does not need to divide the fractional order interval $(0,2)$ into interval $(0,1)$ and interval $[1,2)$ to study them separately. Then, by expanding the dimension of the SFOS, the non-fragile SMO and the sliding surface are constructed and the accurate estimations of faults and the SFOS state simultaneously are achieved. A new reaching law is designed, which can divide the process of the system moving to the sliding surface into three stages. Further the control law is constructed to guarantee the observation error reaches the sliding surface in finite time. Finally, three examples show the effectiveness of the proposed scheme.

Keywords:

• Interval type-2 fuzzy model
• singular fractional order systems
• non-fragile sliding mode observer
• adaptive control law

Acknowledgments

The authors would like to thank the editors and the anonymous reviewers for their constructive comments and suggestions which improved the quality of the paper.

Data availability statement

The data that support the findings of this study are available on request from the corresponding author.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Fundamental Research Funds for the Central Universities [grant number N2224005-3], the National Key Research and Development Program Topic [grant number 2020YFB1710003], the National Natural Science Foundation of China under Grant 62103093 and the Fundamental Research Funds for the Central Universities of China under Grant N2108003.

Notes on contributors

Xuefeng Zhang

Xuefeng Zhang received the B.Sc. degree in applied mathematics, the M.S. degree in control theory and control engineering, and the Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, China, in 1989, 2004, and 2008, respectively. He is currently with the College of Sciences, Northeastern University. He has authored or coauthored more than 200 journal papers and three books. His research interests include fractional order control systems and singular systems. He is an Associate Editor for the Fractal & Fract IET Electronics Letters Journal of the Chinese Institute of Engineers and IEEE ACCESS, and the Committee Member of Technical Committee on Fractional and Control of Chinese Association of Automation.

Jin-Xi Zhang

Jin-Xi Zhang (Member, IEEE) received the B.S. degree in automation and the Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, China, in 2014 and 2020, respectively. From 2019 to 2020, he was a Research Fellow with the Institute for Intelligent Systems, Faculty of Engineering and the Built Environment, University of Johannesburg, Johannesburg, South Africa. He is currently a Distinguished Associate Professor with the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. His research interests include nonlinear control, intelligent control, and image processing.

Wenkai Huang

Wenkai Huang received the B.Sc. degree in mathematics and applied mathematics from Shenyang Normal University in 2017. He is currently pursuing the M.S. degree in operations research and cybernetics with Northeastern University, Shenyang, China. He is also with the College of Sciences, Northeastern University. His research interests include fractional order control systems and robust control.

Peng Shi

Peng Shi (Fellow, IEEE) received the Ph.D. degree in electrical engineering from The University of Newcastle, Callaghan, NSW, Australia, in 1994, the Doctor of Science degree from the University of Glamorgan, Pontypridd, Wales, in 2006, and the Doctor of Engineering degree from The University of Adelaide, Adelaide, SA, Australia, in 2015. He is currently a Professor with The University of Adelaide. His research interests include system and control theory, intelligent systems, and operational research. He has published widely in these areas. Dr. Shi is a Member-at-Large of Board of Governors, the IEEE SMC Society. He is a fellow of the Institution of Engineering and Technology and the Institute of Engineers, Australia. He received the Andrew Sage Best Transactions Paper Award from the IEEE SMC Society in 2016 and the Lotfi Zaden Best Paper Award from the International Conference of Machine Learning and Cybernetics in 2019. He has served on the Editorial Board of a number of journals, including Automatica, the IEEE transactions on automatic control, the IEEE transactions on cybernetics, The IEEE transactions on fuzzy systems, The IEEE transactions on circuits and systems, ieee access, The IEEE control systems letters, Information Sciences, and Signal Processing. He is currently an IEEE Distinguished Lecturer.