基于频域法的二阶多智能体系统快速一致性分析

Fast consensus analysis of second-order multi-agent systems based on frequency domain method

一致性分析是多智能体系统(Multi-agent systems, MASs)理论研究的基本问题,研究目标是为系统中每一个智能体设计合理有效的分布式协议使其实现一致性。以图论为工具,引入矩阵论和稳定性理论等方法,讨论了具有无向拓扑网络结构的二阶MASs快速一致性控制,并基于传统的一致性协议提出了改进的新算法。该算法采用线性系统的频域理论,根据奈奎斯特稳定性判据给出了闭环系统稳定且具有较快收敛速度的充分性条件,克服了常规的Lyapunov稳定性理论分析方法中难以构造Lyapunov函数的不足。提出两个具有不同网络拓扑结构的仿真实例,通过Matlab对算法进行验证,结果发现:与传统算法相比,该算法不仅能够镇定系统,且能显著提高系统的收敛速度,提升系统的平稳性与快速性。

The consistency analysis problem is the fundamental issue of multi-agent systems(MASs) theory, which aims to design a reasonable and effective distributed protocol for each agent in the system so that a group of agents can achieve consensus. The fast consistency control problem of second-order MASs with undirected topological networks was analyzed based on matrix theory, stability theory and graph theory. Besides, an improved new algorithm was obtained on the basis of conventional consistency protocol. The algorithm adopts the frequency domain of linear systems, and gives the sufficient conditions for stable closed-loop system and fast convergence speed based on Nyquist stability criterion. And the new algorithm overcomes the shortcomings of the conventional Lyapunov stability method which is difficult to construct Lyapunov function. Two simulation examples with different topological networks were proposed to verify the proposed algorithm by Matlab. The results show that the proposed algorithm cannot just stabilize the system, but also significantly improve the convergence speed, stability and rapidity of the system.