一种通用的离散时间Altafini模型
A Generalized Discrete-Time Altafini Model
AI总结：
本文研究了一种离散时间模 consensus 模型，探讨了网络代理间交互的时变增益图特性，证明了在适当连通性下，集群会以指数速度收敛，且当增益图序列
摘要：
本文考虑了一种离散时间模 consensus 模型，其中网络代理间的交互由一个时间依赖的增益图描述，该图的顶点对应代理，边赋以从循环群中选取的复数。通过图论方法研究了该模型的极限行为。证明在适当连通性下，若增益图序列
英文摘要：
A discrete-time modulus consensus model is considered in which the interaction among a family of networked agents is described by a time-dependent gain graph whose vertices correspond to agents and whose arcs are assigned complex numbers from a cyclic group. Limiting behavior of the model is studied using a graphical approach. It is shown that, under appropriate connectedness, a certain type of clustering will be reached exponentially fast for almost all initial conditions if and only if the sequence of gain graphs is "repeatedly jointly structurally balanced" corresponding to that type of clustering, where the number of clusters is at most the order of a cyclic group. It is also shown that the model will reach a consensus asymptotically at zero if the sequence of gain graphs is repeatedly jointly strongly connected and structurally unbalanced. In the special case when the cyclic group is of order two, the model simplifies to the so-called Altafini model whose gain graph is simply a signed graph.
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