均值模型下满足对数级收敛速度的动态系统

摘要

In this paper, the convergence time required to achieve consensus of dynamic systems was studied under the uniform averaging model. In each time step, a node’s value was updated to some weighted average of its neighbors’ and its old values. The case was studied when the underlying network was dynamic. Our analysis results show that dynamic networks exhibit fast convergence behavior as long as the nodes’ degrees change gradually, even under very mild connectivity assumptions.%文章研究了在均值模型下，动态系统收敛至一致性状态所需的时间。在每一时间步内，节点计算其邻居的均值，并以计算结果作为自己的新值。我们考虑了当节点间的网络结构处于动态变化状态的情况。我们的分析证明了当节点的度在相邻时间点之间变化较小的情况下，即使仅满足微弱的连通性条件，动态变化的网络仍然可以保证动态系统会快速收敛到一致性状态。