Cluster consensus of high-order multi-agent systems with switching topologies

Abstract

This paper investigates the cluster consensus problems of generic linear multi-agent systems with switching topologies. Sufficient criteria for cluster consensus, which generalise the results in existing literatures, are derived for both state feedback and observer-based control schemes. By using an averaging method, it is shown that cluster consensus can be achieved when the union of the acyclic topologies contains a directed spanning tree within each cluster frequently enough. We also provide a principle to construct digraphs with inter-cluster cyclic couplings that promote cluster consensus regardless of the magnitude of inter-agent coupling weights. Finally, numerical examples are given to demonstrate the effectiveness of the proposed approaches.

Keywords:

• multi-agent systems
• cluster consensus
• high order
• averaging method
• switching topologies

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. See Section 4 for topological conditions that guarantee $\sigma \left({\tilde{L}}_k\right)\subseteq {\mathbb{C}}^{+}$.

2. See Section 3.1 for the definition.

Additional information

Funding

This work is jointly supported by the Specialized Research Fund for the Doctoral Programme of Higher Education [grant number 20110002110015], the National Basic Research Programme of China [grant number 2012CB821206], and the National Natural Science Foundation of China [grant number 61374054], [grant number 61304157], [grant number 61473161], [grant number 61174069], [grant number 51374082].

Notes on contributors

Bo Hou

Bo Hou received his BS and MS degrees from the High-tech Institute of Xi'an in 2009 and 2012. He is now a joint training PhD student of the Department of Computer Science and Technology in Tsinghua University and the Department of Automation in High-tech Institute of Xi'an. His research interests include multi-agent coordination and satellite navigation signal simulation.

Fuchun Sun

Fuchun Sun received his PhD degree from Tsinghua University in China in 1998. He is currently a professor with the Department of Computer Science and Technology, Tsinghua University. His research interests include intelligent control, neural networks, fuzzy systems, nonlinear systems and robotics.

Hongbo Li

Hongbo Li received his PhD degree from Tsinghua University, China, in 2009. He is currently an assistant professor with the Department of Computer Science and Technology, Tsinghua University. His research interests include networked control systems and intelligent control.

Yao Chen

Yao Chen received his BS degree in mathematics from the Three Gorges University, China, in 2007, and his PhD degree from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China, in 2012. Currently, he is a research assistant in the Department of Computing, Hong Kong Polytechnic University. His research interests include complex networks, multi-agent systems, rail traffic control and optimization.

Jianxiang Xi

Jianxiang Xi received his BS, MS and PhD degrees from the High-tech Institute of Xi'an, China, in 2004, 2007 and 2012, respectively. He is currently an associate professor in the High-tech Institute of Xi'an. His research interests include complex systems control, switched systems and multi-agent systems.