Scaled cluster consensus of discrete-time multi-agent systems with general directed topologies

ABSTRACT

This note proposes a notion of scaled cluster consensus, wherein the final consensus states within different clusters converge to prescribed ratios. Unlike most results in existing literature on cluster consensus, no constraints are imposed on the system topologies under the designed protocol, i.e. the agents are not required to possess any cluster affiliation information of others. For the delay-free case, an explicit scaled cluster consensus function is provided by exploring the characteristics of stochastic matrices. Diverse input delays and asymmetric communication delays are both considered, and sufficient condition for scaled cluster consensus is derived based on frequency domain analysis. Finally, numerical examples are given to illustrate the effectiveness of the presented results.

Keywords:

• Scaled cluster consensus
• multi-agent systems
• input delays
• communication delays

Additional information

Funding

This work is jointly supported by the National Basic Research Program of China [grant number 2012CB821206]; the National Natural Science Foundation of China [grant number 61374054], [grant number 61304157], [grant number 61473161], [grant number 61174069], [grant number 51374082]; Tsinghua University Initiative Scientific Research Program [grant number 20131089295].