A survey on state estimation of complex dynamical networks

Abstract

The analysis and synthesis issues have gained widespread attention for complex dynamical networks (CDNs) over the past few years. Accordingly, some challenges including protocol-based scheduling, security vulnerability, limited communication resources as well as network-induced phenomena have to be handled by developing effective analysis and design approaches. In this paper, we make an attempt to review the latest state estimation schemes for CDNs especially those over the networked environment. Firstly, the engineering background and the current attractive topics in regard to CDNs are presented. Subsequently, we provide a review of several types of state estimation methods under different performance indices, for example, $H_{\mathrm{\infty }}$ state estimation, set-membership state estimation, optimal state estimation and fault estimation. Next, particular effort is devoted to show the up-to-date progresses on the protocol-based state estimation and compensation-based state estimation approaches for CDNs. Finally, some challenging problems are outlined regarding the future research to promote the theoretical developments in related fields.

Keywords:

• Complex dynamical networks
• state estimation
• fault estimation
• networked-induced phenomena
• protocol-based communication scheduling

Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Disclosure statement

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

Notes on contributor(s)

Jun Hu received the B.Sc. degree in Information and Computation Science and M.Sc. degree in Applied Mathematics from Harbin University of Science and Technology, Harbin, China, in 2006 and 2009, respectively, and the Ph.D. degree in Control Science and Engineering from Harbin Institute of Technology, Harbin, China, in 2013. From September 2010 to September 2012, he was a Visiting Ph.D. Student in the Department of Information Systems and Computing, Brunel University, U.K. From May 2014 to April 2016, he was an Alexander von Humboldt research fellow at the University of Kaiserslautern, Kaiserslautern, Germany. He is a Professor and Ph.D. supervisor in the Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China. His research interests include nonlinear control, filtering and fault estimation, time-varying systems and complex networks. He has published more than 70 papers in refereed international journals. Prof. Hu serves as a reviewer for Mathematical Reviews, as an editor for Neurocomputing, Journal of Intelligent and Fuzzy Systems, Neural Processing Letters, Systems Science and Control Engineering, and as a guest editor for International Journal of General Systems and Information Fusion.

Chaoqing Jia received the B.Sc. degree in Information and Computation Science and M.Sc. degree in Mathematics from Harbin University of Science and Technology, Harbin, China, in 2015 and 2019, respectively. He is currently pursuing the Ph.D. degree in Operational Research and Cybernetics, Harbin University of Science and Technology, Harbin, China. His research interests include protocol-based state estimation and complex networks. He is a very active reviewer for many international journals.

Hongjian Liu received the B.Sc. degree in Applied Mathematics in 2003 from Anhui University, Hefei, China and the M.Sc. degree in Detection Technology and Automation Equipments in 2009 from Anhui Polytechnic University, Wuhu, China, and the Ph.D. degree in Control Theory and Control Engineering in 2018 from Donghua University, Shanghai, China. He is currently a Professor in the School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, China. His current research interests include filtering theory, memristive neural networks and network communication systems. He is a very active reviewer for many international journals.

Xiaojian Yi received the B.S. degree in control technology from the North University of China, Taiyuan, China, in 2010, and the M.S. and Ph.D. degrees in reliability engineering from the Beijing Institute of Technology, Beijing, China, in 2012 and 2016, respectively. During 2015 and 2016, he was a jointly trained Ph.D. student with the University of Ottawa, Ottawa, ON, 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. He is the author of two books and more than 100 articles, and is also the holder of eight patents. His research interests include system reliability analysis, intelligent control, fault diagnosis and health management.

Yurong Liu received the B.S. degree in Mathematics from Suzhou University, Suzhou, China, in 1986, the M.S. degree in Applied Mathematics from Nanjing University of Science and Technology, Nanjing, China, in 1989, and the Ph.D. degree in Applied Mathematics from Suzhou University, Suzhou, China, in 2001. Dr. Liu is currently a professor with the Department of Mathematics, Yangzhou University, China. He also serves as an Associate Editor of Neurocomputing. So far, he has published more than 100 papers in refereed international journals. His current interests include stochastic control, neural networks, complex networks, nonlinear dynamics, time-delay systems, multi-agent systems and chaotic dynamics.

Additional information

Funding

This paper is supported by the National Natural Science Foundation of China [grant number 12171124], [grant number 61673141]; the Talent Training Project of Reform and Development Foundation for Local Universities from Central Government of China: Youth Talent Project; the Fundamental Research Foundation for Universities of Heilongjiang Province of China [grant number 2019-KYYWF-0215]; the Outstanding Youth Science Foundation of Heilongjiang Province of China [grant number JC2018001]; and the Alexander von Humboldt Foundation of Germany.