🤖 AI Summary
This study investigates how graph gluing strategies influence the convergence rate of consensus in multi-agent systems. Focusing on two interconnection schemes—bridge-based and interface-based gluing—the work employs algebraic graph theory and consensus dynamics to establish a theoretical link among the gluing structure, spectral properties of the graph Laplacian, and system convergence performance. The key contribution lies in elucidating how the number and topology of inter-agent communication links modulate the Fiedler eigenvalue, thereby enabling a quantitative assessment of the enhancement in algebraic connectivity imparted by different gluing mechanisms. Theoretical findings are validated through numerical simulations, offering spectral optimization principles for modular design of multi-agent networks.
📝 Abstract
In this paper, the effects of graph gluing operations in networks of multi-agent systems and their impact on system performance are investigated. In many practical applications, multiple multi-agent subsystems must be interconnected through communication links to accomplish complex tasks, resulting in a larger communication network. Such interconnections modify the underlying graph topology and consequently affect the consensus behavior and convergence rate of the network. In particular, this paper examines both bridge gluing and interface gluing and analyzes how the number and structure of communication links between subsystems influence the Fiedler eigenvalue of the resulting graph. Since the Fiedler eigenvalue is directly related to the convergence rate of consensus dynamics, the proposed analysis establishes a clear relationship between interconnection strategies, algebraic connectivity, and system performance. The results provide theoretical insight into how different gluing mechanisms alter the spectral properties of the graph Laplacian and, in turn, the convergence characteristics of the networked multi-agent system. Simulation studies are presented to illustrate the theoretical findings and to validate the effectiveness of the proposed framework.