Consensus in Networks of Agents with Cooperative and Antagonistic Interactions

Yanping Gao, Kaixuan Kou, Weijing Zhang, Yishu Dai () and Jingwei Ma
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Yanping Gao: School of E-Business and Logistics, Beijing Technology and Business University, Beijing 100048, China
Kaixuan Kou: School of E-Business and Logistics, Beijing Technology and Business University, Beijing 100048, China
Weijing Zhang: School of E-Business and Logistics, Beijing Technology and Business University, Beijing 100048, China
Yishu Dai: School of E-Business and Logistics, Beijing Technology and Business University, Beijing 100048, China
Jingwei Ma: Safety Assessment Guarantee Room, Beijing 100073, China

Mathematics, 2023, vol. 11, issue 4, 1-13

Abstract: This paper studies the consensus of first-order discrete-time multi-agent systems with fixed and switching topology, and there exists cooperative and antagonistic interactions among agents. A signed graph is used to model the interactions among agents, and some sufficient conditions for consensus are obtained by analyzing the eigenvalues of a Laplacian matrix in the case of fixed topology. The results indicate that having a spanning tree is only a necessary condition for the consensus of multi-agent systems with signed graphs, which is also affected by edge weights. Consensus is further discussed in the case of switching topology, and the results reveal that consensus can be reached if the controller gain and the union graphs among some consecutive time intervals satisfy some conditions. Finally, several simulation examples further confirm the theoretical results.

Keywords: multi-agent systems; consensus; signed graphs; antagonistic interaction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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