Leader-following consensus of nonlinear singular multi-agent systems under signed digraph

Abstract

This paper investigates the leader-following consensus problem for a singular multi-agent system with nonlinear dynamics and signed digraph topology. Firstly, an algorithm is proposed to address the structural balance problem of the signed network, which is suitable for all types of signed graphs. Secondly, by using M-matrix theory, the bipartite consensus conditions for the singular nonlinear multi-agent system are established when the topology digraph is structurally balanced. Thirdly, the global asymptotic stability conditions are presented when the signed network is structurally unbalanced. Both the controllers are designed by using pinning control strategies. Finally, numerical examples are given to illustrate the correctness and effectiveness of the proposed methods.

Keywords:

• Multi-agent systems
• singular systems
• signed graph
• leader-following consensus
• pinning control

Disclosure statement

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

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 62073180, 61973177 and 61903203]; the Postgraduate Research & Practice Innovation Program of Jiangsu Province [grant number KYCX18_2421]; the Science and Technology Project of Nantong City [grant number JC2019118]; and the Natural Science Research Projects of Colleges and Universities in Jiangsu Province [grant number 19KJB120011].

Notes on contributors

Jie Ren

Jie Ren received the B.Sc. degree in Information and Computer Science and the M.Sc. degree in Control Theory and Control Engineering from Nantong University, Nantong, China, in 2007 and 2010, respectively. She is currently pursuing Ph.D. degree in Information and Communication Engineering with Nantong University, Nantong, China. She joined Nantong University Xinglin College, Nantong, China, in 2010. Her current research interests are bipartite consensus problems of multi-agent systems under signed digraph.

Qiang Song

Qiang Song received the Ph.D. degree from the School of Automation, Southeast University, Nanjing, China, in 2011. He is currently an Associate Professor with the School of Electrical Engineering, Nantong University, Nantong, China. Dr Song has published over 10 peer-reviewed international journal papers, including three highly cited Essential Science Indicators (ESI) papers on pinning control of networked systems. Dr Song was the outstanding reviewer for IET Control Theory & Application in 2014 and Asian Journal of Control in 2016, respectively. His current research interests include the coordination control and the collective behaviours for complex networks and multi-agent systems.

Yanbo Gao

Yanbo Gao received the M.Sc. degree in Applied Mathematics and the Ph.D. degree in Operation Research and Control Theory from East China Normal University, Shanghai, China. He joined the staff of Nantong University in 2002, and is currently a Professor in the School of Science, Nantong University. His current research interests are chaotic systems, neural networks, time-delay systems, complex systems and complex networks.

Min Zhao

Min Zhao received the B.Sc. degree in applied mathematics and the M.Sc. degree in software engineering from Soochow University, Suzhou, China, in 2002 and 2005, respectively. She is currently pursuing the Ph.D. degree in control science and engineering with Shanghai University, Shanghai, China. She joined Nantong University, Jiangsu, China, in 2002. Her current research interests include networked control systems, event-triggered control systems, and multi-agent systems.

Guoping Lu

Guoping Lu received the B.S. degree from the Department of Applied Mathematics, Chengdu University of Science and Technology, Chengdu, China, in 1984, and the M.S. and Ph.D. degrees in Applied Mathematics from the Department of Mathematics, East China Normal University, Shanghai, China, in 1989 and 1998, respectively. He is currently a Professor with the School of Electrical Engineering, Nantong University, Jiangsu, China. His research interests include singular systems, multi-agent systems, networked control, and nonlinear signal processing.