Cluster consensus in discrete-time networks of multiagents with inter-cluster nonidentical inputs

Area of Science:

• Control Theory
• Networked Systems
• Distributed Computing

Background:

• Multiagent systems require coordinated behavior for complex tasks.
• Achieving consensus within and separation between agent clusters is crucial for decentralized control.
• Existing consensus theories often assume identical inputs or simple network structures.

Purpose of the Study:

• To investigate cluster consensus in multiagent systems with inter-cluster nonidentical inputs.
• To extend existing consensus theories to handle general and time-varying graph topologies.
• To define and achieve both intracluster synchronization and intercluster separation.

Main Methods:

• Extended concepts of consensus theory, including spanning trees and matrix products, for intracluster synchronization.
• Utilized cluster spanning trees and self-linked vertices conditions for static and time-varying systems.
• Employed nonidentical inter-cluster inputs to achieve agent separation.
• Analyzed the boundedness of system trajectories based on input summation.

Main Results:

• Proved that static linear systems can achieve intracluster synchronization under specific graph conditions (cluster spanning trees, self-linked vertices).
• Demonstrated that time-varying systems can also achieve intracluster synchronization with T-interval cluster spanning trees.
• Showcased the effectiveness of nonidentical inter-cluster inputs for achieving inter-cluster separation.
• Established conditions for the boundedness of system trajectories.

Conclusions:

• The proposed methods enable robust cluster consensus, encompassing both synchronization within clusters and separation between them.
• The findings are applicable to general and time-varying network topologies.
• The study provides a framework for designing coordinated multiagent systems with differentiated cluster behaviors, as illustrated by a social learning model.