多智能体系统一致性的递阶结构设计

Hierarchical structure design for multi-agent consensus

针对多智能体系统的一致性协作,研究了以提高群体一致性收敛速度为目标的多层递阶拓扑结构设计问题.首先讨论了满足物理拓扑约束并具有更优性能的递阶拓扑结构存在的可能性.在此基础上,根据一致性问题的收敛时间性能指标,将递阶结构设计转化为一个与多层递阶系统中所有子图拉普拉斯矩阵特征值相关的优化问题.通过将连通图转换为若干点导出子图和它们之间的关联图,提出一个该优化问题的双层拓扑结构设计算法,并基于该算法发展了满足物理拓扑结构约束的多层递阶结构设计算法.仿真算例表明由此设计的递阶协作过程可有效加快多智能体群体一致性的收敛速度.

The hierarchical structure design problem for multi-agent consensus is investigated for optimizing the group cooperation performance.The possibility of finding a hierarchical structure with better performance for multi-agent consensus under given physical topology constraints is discussed.According to the convergence time index of consensus,the hierarchical structure design problem is then converted into an optimization problem involving the Laplacian eigenvalues of all subgraphs in the multi-layer hierarchical structure.A two-layer structure design algorithm is developed by transforming a connected graph to some vertex-induced subgraphs and their interconnection graph.Based on this algorithm,a multi-layer hierarchical structure design algorithm is derived for multi-agent consensus under given physical communication topology constraints.Moreover,numerical simulations are provided to demonstrate that the consensus velocity can be improved effectively by the developed hierarchical cooperation scheme.