Complex Laplacians and Applications in Multi-Agent Systems

2014/06/07 by Jiu‐Gang Dong, Li Qiu, Dong, Jiu-Gang +1 · 1 citation
Computer Science · Medicine · #Distributed Control Multi-Agent Systems #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Neural Networks Stability and Synchronization #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1406.1862

openalex publication_date 2014/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Complex-valued Laplacians have been shown to be powerful tools in the study of distributed coordination of multi-agent systems in the plane including formation shape control problems and set surrounding control problems. In this paper, we first provide some characterizations of complex Laplacians. As an application, we then establish some necessary and sufficient conditions to ensure that the agents interacting on complex-weighted networks converge to consensus in some sense. These general consensus results are used to discuss some multi-agent coordination problems in the plane.

Citations

• Consensus Problems in Networks of Agents With Switching Topology and Time-Delays
• Consensus and Cooperation in Networked Multi-Agent Systems

Cited by

• Laplacian Flows in Complex-valued Directed Networks: Analysis, Design, and Consensus

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