Achieving Cluster Consensus in Continuous-Time Networks of Multi-Agents With Inter-Cluster Non-Identical Inputs

TL;DR

This paper investigates how multi-agent networks with time-varying connections can achieve cluster consensus through adaptive inputs, ensuring agents within the same cluster synchronize while different clusters remain separated.

Contribution

It introduces a novel approach using adaptive inputs and inter-cluster common influence to achieve cluster consensus in continuous-time multi-agent networks.

Findings

Cluster consensus is achievable with the proposed adaptive input method.

The $ ext{delta}$-cluster-spanning-tree condition is key for intra-cluster synchronization.

Simulation results confirm the theoretical analysis.

Abstract

In this paper, cluster consensus in continuous-time networks of multi-agents with time-varying topologies via non-identical inter-cluster inputs is studied. The cluster consensus contains two aspects: intra-cluster synchronization, that the state differences between agents in the same cluster converge to zero, and inter-cluster separation, that the states of the agents in different clusters do not approach. $\delta$-cluster-spanning-tree in continuous-time networks of multi-agent systems plays essential role in analysis of cluster synchronization. Inter-cluster separation can be realized by imposing adaptive inputs that are identical within the same cluster but different in different clusters, under the inter-cluster common influence condition. Simulation examples demonstrate the effectiveness of the derived theoretical results.