I&I adaptive fault-tolerant control of a class of nonaffine systems with nonlinearly parameterised faults

AbstractThis paper provides a novel fault-tolerant control scheme for a class of nonaffine systems with nonlinearly parameterised (NLP) faults. The nonaffine system is firstly transformed into an augmented one via dynamic feedback control. A fault-tolerant controller with Immersion and Invariance (I&I) adaptation law is designed for the transformed system through dynamic surface control. The controller avoids complexity due to the explosion of terms in backstepping design. The I&I adaptation law is developed to recover the unknown parameters of NLP faults in the system. The proposed scheme can shape the transient performance of the parameter estimation error and tracking error. In the tracking problem, all the signals and tracking error converge exponentially to a small neighbourhood of the origin. In the regulation problem, the system output converges exponentially to zero. A numerical simulation is carried out to verify the effectiveness of the proposed scheme.Keywords: Immersion and invariance manifolddynamic feedback controldynamic surface controlnonaffine systemsnonlinearly parameterisation Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by the Fundamental Research Funds for the Central Universities [grant number 2022YJS021] and [grant number 2022JBZY001]; the National Natural Science Foundation of China [grant number 62371032].Notes on contributorsMin ZhangMin Zhang received her B.S. degree from Zhengzhou University, China, in 2019. She is currently working toward the Ph.D. degree in control science and engineering with Beijing Jiaotong University, Beijing, China. Her main research interests include adaptive control, nonlinear control and fault-tolerant control.Xiangbin LiuXiangbin Liu received his B.S. degree from Xi'an Institute of Technology, China, in 1995, M.S. degree from University of Science and Technology Beijing, China, in 2002, and Ph.D. degree from Zhejiang University, China, in 2009, respectively. He is currently an Associate Professor with Beijing Jiaotong University (BJU). His research interests include adaptive control, robust control and nonlinear control.Xiaoyu ZhangXiaoyu Zhang (Senior Member, IEEE) was born in 1978. He received the B.S. degree from Yanshan University, in 2000, and the M.S. and Ph.D. degrees from Zhejiang University, in 2003 and 2006, respectively. From 2006 to 2007, he was with the School of Information Science and Engineering, Nanchang University. From 2007 to 2021, he has been taught with the North China Institute of Science and Technology (NCIST). From 2018 to 2019, he was a Visiting Scholar with Columbia University, New York. He is currently a Professor with Beijing University of Civil Engineering and Architecture (BUCEA). His research interests include nonlinear control, intelligent control, switching systems, driving systems, power electronics, and complex systems.Hongye SuHongye Su (Senior Member, IEEE) was born in 1969. He received the B.S. degree in industrial automation from the Nanjing University of Chemical Technology, Nanjing, China, in 1990 and the M.S. and Ph.D. degrees in industrial automation from Zhejiang University, Hangzhou, China, in 1993 and 1995, respectively. From 1995 to 1997, he was a Lecturer with the Department of Chemical Engineering, Zhejiang University. From 1998 to 2000, he was an Associate Professor with the Institute of Advanced Process Control, Zhejiang University, where he is currently a Professor with the Institute of Cyber-Systems and Control. His current research interests include robust control, time-delay systems, and advanced process control theory and applications.