Convergence speed of consensus problems over undirected scale-free networks

Abstract

Scale-free networks and consensus behaviour among multiple agents have both attracted much attention. To investigate the consensus speed over scale-free networks is the major topic of the present work. A novel method is developed to construct scale-free networks due to their remarkable power-law degree distributions, while preserving the diversity of network topologies. The time cost or iterations for networks to reach a certain level of consensus is discussed, considering the influence from power-law parameters. They are both demonstrated to be reversed power-law functions of the algebraic connectivity, which is viewed as a measurement on convergence speed of the consensus behaviour. The attempts of tuning power-law parameters may speed up the consensus procedure, but it could also make the network less robust over time delay at the same time. Large scale of simulations are supportive to the conclusions.

Average consensus of multi-agent systems with communication time delays and noisy links

“…If we choose ε 1 > K 1 ε 2 and can find two positively definite matrices , for < 0, then setting −λ = λ max ( ) (λ > 0), we obtain from inequalities (17) and (19) that…”

“…In recent years, a number of researchers have investigated the consensus problems from various perspectives. [15][16][17][18][19][20][21] In multi-agent systems, communication time delays may arise naturally, e.g., because of agents moving, the congestion of the communication channels, and the asymmetry of the interactions. Therefore, the stability analysis for multiagent systems with time delays has become an attractive subject of research in the past few years.…”

Ising model on evolution networks and its application on opinion formation

“…The emergence of social behavior at the global population level has been widely studied. [1][2][3][4][5][6][7][8][9] The application of the statistical physics models to social dynamics is called sociophysics. [10,11] With statistical analysis of networks, the physics of networks [12] becomes a new field, and supplies important clues about how networks function and even offers predictions of their future behavior.…”

Leader—following consensus control for networked multi-teleoperator systems with interval time-varying communication delays

“…Recently, the consensus problem has been studied in various fields, such as groups of mobile autonomous agents, [2] networked control systems, [3] and other applications. [4][5][6][7][8][9][10] In Refs. [11] and [12], the consensus problems for high-order multi-agent systems were studied.…”