Invariant set-based robust fault detection and optimal fault estimation for discrete-time LPV systems with bounded uncertainties

ABSTRACT

This paper proposes an invariant set-based robust fault detection (FD) and optimal fault estimation (FE) method for discrete-time linear parameter varying (LPV) systems with bounded uncertainties. Firstly, a novel invariant-set construction method for discrete-time LPV systems is proposed if and only if the system is poly-quadratically stable, which need not satisfy the condition that there must exist a common quadratic Lyapunov function for all vertex matrices of the system compared to the traditional invariant-set construction methods. Furthermore, by using a shrinking procedure, we provide minimal robust positively invariant (mRPI) set approximations that are always positively invariant at each step of iteration and allow a priori desired precision to obtain a high sensitivity of FD. Owing to the existence of invariant set-based FD phase, the assumption that the initial faults should be bounded by a given set can be avoided for FE. We compute an optimal parametric matrix gain by minimising the Frobenius norm-based size of the corresponding FE set to obtain the optimal FE performance. Theoretically, any trajectory in the FE tube can be chosen as a specific-value estimation for the real fault signals. Finally, a vehicle dynamics system is used to illustrate the effectiveness of the proposed method.

Keywords:

• Fault detection
• fault estimation
• invariant set
• zonotopic Kalman filter
• discrete-time LPV systems

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Junbo Tan http://orcid.org/0000-0002-8956-5408

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China (no. 61803221), the Science and Technology Planning Project of Guangdong Province (no. 2017B010116001), and the Basic Research Program of Shenzhen (JSGG20160301100206969 and JCYJ20170412171459177).

Notes on contributors

Junbo Tan

Junbo Tan received the bachelor’s degree from the Department of Management and Engineering, Nanjing University, Nanjing, China, in 2013, and the master’s degree from the Department of Automation, Tsinghua University, Beijing, China, in 2016 where he is currently pursuing the Ph.D. degree with the Navigation and Control Research Center. His research interests include fault diagnosis, linear parameter-varying systems, and Faulttolerant control.

Feng Xu

Feng Xu received the bachelor’s degree (Hons.) in measurement and control technology and instruments from North western Polytechnical University (NWPU), Xi’an, China, in July 2010, and the Ph.D. degree (Hons.) in automatic control from the Technical University of Catalonia (UPC), Barcelona, Spain, in November 2014. From January to April 2014, he was a Visiting Ph.D. student with the Centrale-Supélec, Paris, France. Since March 2015, he has been an Assistant Professor with Tsinghua University, China. His research interests include fault diagnosis, fault-tolerant control, and model predictive control and their applications.

Xueqian Wang

Xuwqian Wang received his Master’s and Ph.D. degrees in Control Science and Engineering both from Harbin Institute of Technology (HIT), Harbin, P.R. China, in 2005 and 2010, respectively. From June 2010 to February 2014, he was a Postdoctoral Researcher at HIT. Since March 2014, he is currently an Associate Researcher and the leader of the Center for Artificial Intelligence and Robotics, Graduate School at Shenzhen, Tsinghua University. His Research interests include Dynamics, Control and Teleoperation.

Jun Yang

Jun Yang received the bachelor’s degree from the Department of Marine Science and Technology, Northwestern Polytechnical University, Xi’an, China, in 2004, and the master’s degree from the Department of Automation, Beijing University of Posts and Telecommunication, Beijing, China, in 2007, the doctor’s degree from the Department of Automation, Tsinghua University, Beijing, China, in 2011. His research interests include deep reinforcement learning, fault diagnosis, and sensor technology.

Bin Liang

Bin Liang received the bachelor’s and master’s degrees from the Honors College, Northwestern Polytechnical University, Xi’an, China, in 1989 and 1991, respectively, and the Ph.D. degree from the Department of Precision Instrument, Tsinghua University, Beijing, China, in 1994. From 1994 to 2003, he was a Postdoctoral Researcher, an Associate Researcher, and a Researcher with the China Academy of Space Technology. From 2003 to 2007, he was a Researcher and an Assistant Chief Engineer with China Aerospace Science and Technology Corporation. Since 2007, he has been a Professor with the Department of Automation, Tsinghua University. He has authored and coauthored over 100 articles in international journals and conference proceedings. His research interest includes modeling and control of dynamic systems and their applications to space robots and satellites.