Recursive filtering of networked nonlinear systems: a survey

Abstract

Recursive filtering for nonlinear systems, one of the core technologies of modern industrial systems, is an ever-increasing research topic from the control and computer communities. Some challenges from communication scheduling, limited bandwidth as well as security vulnerability have to be seriously handled though the applications of communication technologies bring into some conveniences. As such, it is of utmost significance in theory and great importance in applications to establish engineering-feasible recursive filtering algorithms for networked nonlinear systems. This paper focuses on the development of this topic and provides an up-to-date survey of the existing nonlinear filtering techniques. The introduction of three classes of communication protocols is first presented in great detail, and then comprehensive reviews and summaries of the nonlinear recursive filtering problems with Gaussian/non-Gaussian noises are elaborated according to different strategies responding to nonlinear functions or noises. Particularly, the reviews are layout from the extended Kalman filtering, the unscented/cubature Kalman filtering, the set-membership filtering as well as the $H_{\mathrm{\infty }}$ filtering. Furthermore, several challenging issues are raised to stimulate further related theoretical research and practical applications in this field.

Keywords:

• Nonlinear systems
• recursive filtering
• communication protocols
• cyber-attacks

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grants 61973219 and 61933007, in part by the Natural Science Foundation of Shanghai under Grant 18ZR1427000.

Disclosure statement

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

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China under Grants 61973219 and 61933007, in part by the Natural Science Foundation of Shanghai under Grant 18ZR1427000.

Notes on contributors

Jingyang Mao

Jingyang Mao received the B.Sc. degree in mathematics and applied mathematics from University of Shanghai for Science and Technology, Shanghai, China, in 2015, where he is currently pursuing the Ph.D. degree in control science and engineering. He is currently a Research Associate with the Department of Electrical and Computer Engineering, Louisiana State University, Baton Rouge, LA, USA. His research interests include networked control systems as well as protocol-based recursive filtering for nonlinear systems. Dr. Mao is also a very active reviewer for many international journals.

Ying Sun

Ying Sun received the B.Sc. degree in Physics from Harbin Normal University, Harbin, China, in 2013. She is currently pursuing the Ph.D. degree in control science and engineering from University of Shanghai for Science and Technology, Shanghai, China. She is an active reviewer for many international journals. Her current research interests include networked control systems, stochastic control and filtering as well as $H_{\mathrm{\infty }}$, ${\ell }_2$-${\ell }_{\mathrm{\infty }}$ control and filtering.

Xiaojian Yi

Xiaojian Yi was born in 1987. He received the B.S. degree in control technology in 2010 from the North University of China, Taiyuan, China, and the M.S. degree in 2012 and Ph.D. degree in 2016 both in reliability engineering from Beijing Institute of Technology, Beijing, China. During 2015–2016, he was a jointly trained PhD student in the University of Ottawa, Canada, to study robot reliability and maintenance. From 2016 to 2020, he was an Associate Professor with the China North Vehicle Research Institute. He is currently an Associate Professor with the Beijing Institute of Technology, Beijing, China. He is the author of two books and more than 100 articles, and is also the holder of 8 patents. His research interests include system reliability analysis, intelligent control, fault diagnosis and health management.

Hongjian Liu

Hongjian Liu received his B.Sc. degree in applied mathematics in 2003 from Anhui University, Hefei, China, and the M.Sc. degree in detection technology and automation equipment in 2009 from Anhui Polytechnic University, Wuhu, China, and the Ph.D. degree in control science and engineering in 2018 from Donghua University, Shanghai, China. In 2016, he was a Research Assistant with the Department of Mathematics, Texas A&M University at Qatar, Doha, Qatar, for two months. From March 2017 to March 2018, he was a Visiting Scholar in the Department of Information Systems and Computing, Brunel University London, UK. He is currently a Professor in the School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, China. Dr. Liu’s current research interests include filtering theory, memristive neural networks, and network communication systems. He is a very active reviewer for many international journals.

Derui Ding

Derui Ding received both the B.Sc. degree in Industry Engineering in 2004 and the M.Sc. degree in Detection Technology and Automation Equipment in 2007 from Anhui Polytechnic University, Wuhu, China, and the Ph.D. degree in Control Theory and Control Engineering in 2014 from Donghua University, Shanghai, China. From July 2007 to December 2014, he was a teaching assistant and then a lecturer in the Department of Mathematics, Anhui Polytechnic University, Wuhu, China. He is currently a Senior Research Fellow with the School of Software and Electrical Engineering, Swinburne University of Technology, Melbourne, Australia. From June 2012 to September 2012, he was a research assistant in the Department of Mechanical Engineering, the University of Hong Kong, Hong Kong. From March 2013 to March 2014, he was a visiting scholar in the Department of Information Systems and Computing, Brunel University London, UK. His research interests include nonlinear stochastic control and filtering, as well as multi-agent systems and sensor networks. He has published around 80 papers in refereed international journals, and received The 2020 IEEE Systems, Man, and Cybernetics Society Andrew P. Sage Best Transactions Paper Award, and the IET Control Theory and Applications Premium Award 2018. He is serving as an Associate Editor for Neuro computing and IET Control Theory & Applications. He is also a very active reviewer for many international journals. Dr. Ding is serving as an Associate Editor for Neuro computing. He is also a very active reviewer for many international journals.