具有时滞状态导数反馈的一阶多智能体系统的收敛速度分析

Convergence Speed Analysis of First Order Multi-agent Systems Based on Delayed-state-derivative Feedback

对于一阶多智能体系统,提出一类具有加权项的时滞状态导数反馈一致性协议,研究在无向通讯拓扑下多智能体系统实现一致性的收敛速度。给出了多智能体系统在一致性协议下的闭环形式,并利用拉普拉斯矩阵将其转化成紧凑形式;利用矩阵理论,分析反馈强度对闭环形式极点的影响,证明当多智能体系统为超临界时滞多智能体系统时,引入适当的反馈强度可以提高多智能体系统实现一致性的收敛速度;数值仿真验证了结果的有效性。

For first-order multi-agent systems,a class of delayed-state-derivative feedback consensus protocols with weighted terms is proposed,and the convergence rate of multi-agent systems is studied under undirected communication topology.The closed-loop form of multi-agent system under consistency protocol is given,and it is transformed into compact form by Laplacian matrix.Then,the influence of feedback intensity on the poles of closed-loop form is analyzed by using matrix theory.It is proved that when the multi-agent system is a multi-agent system with supercritical time-delay,introducing appropriate feedback intensity can improve the convergence speed of to achieve consistency the multi-agent system.Numerical simulation verifies the effectiveness of the results.