Cluster consensus with first and higher-order antagonistic interaction dynamics - CİHAN, ONUR (My University, 2023)
© 2023 Elsevier B.V.This paper studies the cluster consensus problem for networks with antagonistic interactions modelled by adjacency matrices with negative weights. By introducing an extended digraph representation consisting of purely cooperative interactions with lifting approach, we relate the trajectories of the system to those of an extended system with a positive digraph. The behaviours of agents in a signed network are extracted from its extended digraph. Consequently, the number of clusters and the cluster members are explicitly determined for any signed digraph by using primary and secondary layer subgraph concepts. The relation between the dynamics of a signed system and its extended representation is investigated for first and higher-order systems. The conditions that make both systems stable are stated. Additionally, the control parameters to achieve cluster consensus are derived explicitly for first, second and third order systems. The obtained results for continuous-time networks are subsequently extended to discrete-time networks. Finally, theoretical results are illustrated via numerical examples.
Keywords: Bilgisayar Bilimleri; Algoritmalar; Yaşam Bilimleri; Temel Bilimler; Mühendislik ve Teknoloji; Computer Sciences; algorithms; Life Sciences; Natural Sciences; Engineering and Technology; Mühendislik, Bilişim ve Teknoloji (ENG); Yaşam Bilimleri (LIFE); Bilgisayar Bilimi; Sinirbilim ve Davranış; BİLGİSAYAR BİLİMİ, YAPAY ZEKA; SİNİR BİLİMİ; Engineering, Computing & Technology (ENG); Life Sciences (LIFE); COMPUTER SCIENCE; NEUROSCIENCE & BEHAVIOR; COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE; NEUROSCIENCES; Bilgisayar Bilimi Uygulamaları; Fizik Bilimleri; Bilişsel Sinirbilim; Yapay Zeka; Computer Science Applications; Physical Sciences; Cognitive Neuroscience; Artificial Intelligence; Antagonistic interactions; Cluster consensus; Consensus protocols; Multi-agent systems; Signed digraphs