Group consensus of multi-agent systems in directed networks with noises and time delays

Abstract

In this paper, group consensus problems in fixed directed networks of dynamic agents are investigated. Group consensus means that the agents in each group share a consistent value while there is no agreement between any two groups. Based on algebraic graph theory, sufficient conditions guaranteeing group consensus under the proposed control protocol in the presence of random noises and communication delays are derived. The analysis uses a stability result of Mao for stochastic differential delay equations, which ensures the consensus can be achieved almost surely and exponentially fast. Numerical examples are provided to demonstrate the availability of the obtained results as well as the effect of time delay/noise intensity.

Keywords:

• group consensus
• multi-agent system
• directed graph
• noise
• communication delay

Acknowledgements

I appreciate the editor and reviewers for their careful and helpful concerns.

Additional information

Notes on contributors

Yilun Shang

Yilun Shang received his PhD degree in Mathematics from Shanghai Jiao Tong University, Shanghai, China in 2010. He worked at the Institute for Cyber Security in the University of Texas at San Antonio from 2010 to 2013 as a research fellow. Since 2013, he has worked at Singapore University of Technology and Design, Singapore, where he is currently a research fellow. His research interests include random graph, probabilistic combinatorics, complex network and system, epidemic dynamics, agent-based modelling and control. He is an invited reviewer for Mathematical Reviews and Zentralblatt MATH.