Cluster consensus in first and second-order continuous-time networks with input and communication delays

Abstract

In this paper, we investigate the cluster consensus problem for first and second-order multi-agent systems with or without delay in continuous-time. Contrary to previous studies on cluster consensus in the literature, the clusters are assumed not to be pre-determined. One of the main contributions of the paper is to compute the number and members of the clusters for a first-order multi-agent network evolving over an arbitrary directed graph. Another novel result is its extension to systems with second-order dynamics. The effect of input and communication delay on cluster consensus is also studied in detail and it is shown that there is an upper bound of input delay whereas communication delay does not adversely alter the cluster consensus properties. Theoretical results are illustrated via several simulations.

Keywords:

• Distributed consensus
• cluster consensus algorithms
• multi-agents systems
• first-order systems
• second-order systems
• time-delay systems

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ümit Develer http://orcid.org/0000-0002-6838-8676

Mehmet Akar http://orcid.org/0000-0002-0166-9932

Additional information

Funding

This work was sponsored by Scientific and Technical Research Council of Turkey (Türkiye Bilimsel ve Teknolojik Araştirma Kurumu) under TUBITAK Grant 118E218.