群平衡化赋权有向图/无向图的分布式算法研究

Distributed Strategies for Group-Balancing General Weighted Directed/Undirected Graphs

摘要: 解决多智能体系统一致性协调控制的关键问题是设计合适的协议或算法使得多智能体的状态最终达到一致。己有的理论结果说明一些图平衡条件，如平衡条件和群平衡条件，是解决多智能体系统平均一致性问题和群平均一致性问题的一个必要条件。因此怎样平衡化和群平衡化一个一般图是一个值得研究的问题。然而目前涉及到如何平衡化和群平衡化一个一般图的结果还很少。本文针对有向拓扑图和无向拓扑图，分别提出两种不同的群平衡化算法，并从理论分析和数值仿真两方面验证两种算法的有效性。

Abstract: A key problem of solving the consensus coordination control of multi-agent systems is to design appropriate protocols or algorithms which guarantee the agents reaching consensus. Although existing theoretical results have illustrated the balance conditions and the group-balance condi-tions are necessary when it comes to average consensus and group average consensus respectively, there are few results on how to balance and group-balance a general graph. In this paper, we design two distributed algorithm to group-balance directed and undirected graphs respectively, and prove the validity of the algorithms via both theoretical analysis and example illustrations.