Disturbance estimation-based resilient control design for interval type-2 fuzzy stochastic systems under multiple disturbance observer

Abstract

This research endeavour's primary attention is on the problems of stabilization and multiple disturbance rejection for a class of interval type-2 fuzzy stochastic systems that are prone to parameter uncertainties and multiple disturbances. Specifically, the multiple disturbances are classified into two aspects: the first aspect is matched disturbances, which emanate from an exogenous system, while the second aspect is norm-bounded mismatched disturbances. Further, to provide a precise estimation of the matched disturbances, a fuzzy rule-based multiple disturbance observer is built. Based on the estimated information from the framed observer, a disturbance estimation-based resilient control is devised that can withstand the effects of disturbances. Besides, the footprints of mismatched kind of disturbances are handled by employing the $(\mathcal{Q},\mathcal{S},\mathcal{R})-\tilde{\varsigma }$ dissipative performance. Moreover, to insure the attainment of the foremost objective of this analysis, a collection of suitable criteria has been developed by means of linear matrix inequalities with the satisfied disturbance attenuation index through Lyapunov's theory of stability. In addition, under the lighting of adequate conditions, the gain matrices of the configured controller and the framed observer can be determined. Finally, two simulation examples are supplied as a conclusion to the examination, each serving to illustrate the potency and viability of the designed control scheme and the presented theoretical findings.

Keywords:

• IT2 fuzzy stochastic system
• parameter uncertainties
• multiple disturbances
• multiple disturbance observers
• resilient control

Disclosure statement

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

Data Availability Statement

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

Additional information

Notes on contributors

S. Aarthi

S. Aarthi received the B.Sc. degree in mathematics from Bharathiar University, Coimbatore, Tamil Nadu, India, in 2016, the M.Sc. degree in mathematics from University of Madras, Chennai, Tamil Nadu, India, in 2018 and M. Phil. degree in mathematics from Anna University, Chennai, Tamil Nadu, India, in 2019. She is currently pursuing her Ph.D. degree in the Department of Mathematics, Anna University Regional Campus Coimbatore, Coimbatore, Tamil Nadu, India. Her current research interests include stochastic systems and robust control theory.

T. Satheesh

T. Satheesh received the B.Sc., and M.Sc., degrees in mathematics from Bharathiar University, Coimbatore, Tamil Nadu, India, in 2017 and 2019, respectively. He pursued his Ph.D. degree in the Department of Applied Mathematics, Bharathiar University, Coimbatore, Tamil Nadu, India. He is currently an assistant professor in mathematics with the Karpagam Academy of Higher Education, Coimbatore, India. His current research interests include periodic systems, chaotic systems, power systems and robust control theory.

R. Sakthivel

R. Sakthivel received the B.Sc., M.Sc., M.Phil. and Ph.D. degrees in mathematics from Bharathiar University, Coimbatore, India, in 1992, 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 400 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 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 $\mathrm{\&}$ Technology and International Journal of Applied Mathematics $\mathrm{\&}$ Computer Science.

S. Marshal Anthoni

S. Marshal Anthoni received the M.Sc. and Ph.D. degrees in mathematics from Bharathiar University, Coimbatore, India, in 1995 and 2001, respectively. He was a lecturer with the Department of Mathematics, Kumaraguru College of Technology, Coimbatore, from 2001 to 2003. From 2003 to 2004, he was a postdoctoral fellow with the Department of Mathematics, Yonsei University, South Korea. After that, he was a lecturer with the Department of Mathematics, Periyar University, Salem, India, from 2004 to 2008. He is currently an associate professor in mathematics with the Anna University Regional Campus, Coimbatore. His research interests include control theory and abstract differential equations. He is an active reviewer member of various SCI/SCIE journals.