Observer-based fault tolerant control design for periodic piecewise time-varying systems: a fault estimation approach

ABSTRACT

This study tackles the fault estimation issue for a continuous-time periodic piecewise time-varying systems (PPTVSs) with delays, fault signal and external disturbances. In particular, the PPTVSs are conjured up by segmenting the fundamental period of the periodic system into a finite number of subintervals. Moreover, fault estimator is designed in line with periodic piecewise observer systems to estimate the immeasurable states of the PPTVSs and the fault signal, simultaneously. Subsequently, in accordance with the estimated values of the fault signal and state dynamics, a fault-tolerant controller is devised. Moreover, by utilising Lyapunov stability theory and matrix polynomial lemma, sufficient criteria are procured in context of linear matrix inequalities to affirm the uniform boundedness of the undertaken system and error system. Further, relying on the acquired constraints, the precise configuration of the fault-tolerant control and observer gain matrices are proffered. Eventually, by offering two illustrative examples including mass-spring-damper system, the utility and potential of presented theoretical insights are validated.

KEYWORDS:

• Periodic piecewise time-varying systems
• external disturbances
• time-varying delay
• adaptive fault estimation
• fault-tolerant control

Acknowledgments

This work of R. Sakthivel and N.Aravinth was financially supported by Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India under Core Research Grant (CRG), Sanction No. CRG/2020/002844.

Availability of data and material

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

Compliance with ethical standards

Disclosure statement

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

Additional information

Notes on contributors

R. Sakthivel

R. Sakthivel received the M.Sc., M.Phil., and Ph.D. degrees in Mathematics from Bharathiar University, Coimbatore, India, in 1994, 1996, and 1999, respectively. He served as a Lecturer with the Department of Mathematics, Sri Krishna College of Engineering and Technology, Coimbatore, from 2000 to 2001. From 2001 to 2003, he was a Post-Doctoral Fellow with the Department of Mathematics, Inha University, Incheon, South Korea. From 2003 to 2005, he was a Japan Society for the Promotion of Science (JSPS) Fellow with the Department of Systems Innovation and Informatics, Kyushu Institute of Technology, Kitakyushu, Japan. He was a Research Professor with the Department of Mathematics, Yonsei University, Seoul, South Korea, till 2006. He was a Post-Doctoral Fellow (Brain Pool Program) with the Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang, South Korea, from 2006 to 2008. He served as an Assistant and Associate Professor with the Department of Mathematics, Sungkyunkwan University, Suwon, South Korea from 2008 to 2013. From 2013 to 2016, he was a Professor at the Department of Mathematics, Sri Ramakrishna Institute of Technology, India. He is currently a Professor with the Department of Applied Mathematics, Bharathiar University, Coimbatore, India, since 2016. He has published over 430 research papers in reputed Science Citation Index journals. His current research interests include systems and control theory, optimization techniques, and nonlinear dynamics. He jointly with his foreign research collaborators, published a book and a good number of book chapters in Springer. He has visited Japan, Malaysia, South Korea, Brazil, Germany, Australia, China and Saudi Arabia as a Visiting Researcher. He has continuously received the most coveted “Highly Cited Researcher” Award for the 4 years 2017, 2018, 2019 and 2020, consecutively from the Clarivate Analytics, USA. He has been on the Editorial Board of international journals, including IEEE Access, Journal of the Franklin Institute, Neurocomputing, Neural Processing Letters, Mathematics, Journal of Electrical Engineering & Technology and International Journal of Applied Mathematics and Computer Science.

N. Aravinth

N. Aravinth received the B.Sc., M.Sc., and M.Phil., degree in Mathematics from Bharathiar University, Coimbatore, Tamilnadu, India, in 2017, 2019 and 2021, respectively. He is currently pursuing his Ph.D. degree in the Department of Applied Mathematics, Bharathiar university, Coimbatore, Tamil Nadu, India. His current research interests include periodic systems and robust control theory.

V. Thilagamani

V. Thilagamani received the B.Sc., M.Sc., and M.phil., degree in Mathematics from Bharathiar University, Coimbatore, Tamilnadu, India, in 2015, 2017 and 2019, respectively. She is currently pursuing her Ph.D. degree in the Department of Mathematics, PSGR Krishanmmal College for women, affiliated with Bharathiar university, Coimbatore, Tamil Nadu, India. Her current research interests include periodic systems and robust control theory.

R. Sasirekha

R. Sasirekha has done her under graduation and post-graduation in the field of Mathematics during 1994-1997 and 1997-1999 from Sri GVG Visalakshi College for women, Udumalpet, Bharathiar University, Coimbatore, Tamilnadu, India. She received her M.Phil., and Ph.D. degree from the Department of Mathematics, Bharathiar University, in 2001 and 2017. She is currently an Assistant Professor with the Department of Mathematics, PSGR Krishnammal College for women, Coimbatore, India. Her current research interests include discrete-time neural networks, switched systems and complex dynamical networks.