【作者】 李娜；

【导师】 樊渊；

【作者基本信息】 安徽大学 ， 控制科学与工程， 2024， 硕士

【摘要】 近年来,标量加权多智能系统的二分一致问题得到了广泛而有效的研究。然而,系统往往是错综复杂的,矩阵加权的多智能体系统更具现实意义。现如今对于矩阵加权多智能体系统二分一致性的研究并不多,但吸引了越来越多的学者们进行探索。本论文对矩阵加权网络下多智能体系统的二分一致问题进行了深入研究,主要用到的是代数图论、结构平衡理论、矩阵理论和李雅普诺夫稳定性理论,并且主要研究内容如下:(1)提出一种新的思路来分析矩阵加权多智能体系统,经过理论分析和实验证明得到,可以将矩阵加权多智能体系统的二分一致问题分解成标量加权多智能体系统的群-二分一致问题。由于标量加权多智能体系统的研究已经基本成熟,而且标量加权系统更为简单。因此,借助已有的标量加权系统稳定性、收敛性等方面的理论结果,可以为矩阵加权系统的分析提供有利的指导依据。(2)对于符号网络下的矩阵加权多智能体系统,在实际情况中,智能体之间往往需要交换定向的信息。因此,在对基础的无向通信拓扑系统进行分析后,本论文研究了有向通信拓扑系统的二分一致性。提出了二分一致算法,并利用李雅普诺夫稳定性理论推导出有向多智能体系统实现二分一致的相关条件。最后,用MATLAB进行仿真,实验结果验证了分析结果的正确性。(3)为了可以提高系统整体效率和性能,本论文还研究了含领导智能体的矩阵加权多智能体系统的二分一致问题。首先提出了领导-跟随二分一致控制协议。接着,在无向和有向两种通信拓扑结构下进行研究。在确保结构平衡的前提下,利用李雅普诺夫稳定性理论推导出了实现矩阵加权多智能体系统领导-跟随二分一致的相关条件。最后,同样用MATLAB进行仿真验证。更多还原

【Abstract】 In recent years,the bipartite consensus of scalar-weighted multi-agent systems has been extensively and effectively studied.However,systems are often complex,and matrix-weighted multi-agent systems are more practically significant.Nowadays,there are few researches on the bipartite consensus of matrix-weighted multi-agent systems,but it has attracted an increasing number of scholars to explore.In this paper,the bipartite consensus of multi-agent systems under matrix-weighted networks is deeply studied,mainly using algebraic graph theory,structural balance theory,matrix theory and Lyapunov stability theory,and the main research contents are as follows:(1)A new approach is proposed to analyze matrix-weighted multi-agent systems.Through theoretical analysis and experimental proof,the bipartite consensus of matrix-weighted multi-agent systems can be decomposed into group-bipartite consensus of scalar-weighted multi-agent systems.Because the research of scalar-weighted multi-agent system has been basically mature,and the scalar-weighted system is simpler.Therefore,with the existing theoretical results of stability and convergence of scalar-weighted systems,it can provide a favorable guiding basis for the analysis of matrix-weighted systems.(2)For matrix-weighted multi-agent systems under signed networks,it is often necessary to exchange directional information between agents in practical situations.Therefore,after analyzing the basic undirected communication topological system,this thesis focuses on the bipartite consensus of directed communication topological system.The bipartite consensus algorithm is proposed,and the relevant conditions for the realization of bipartite consensus in directed multi-agent systems are deduced by using Lyapunov stability theory.Finally,MATLAB is used for simulation,and the experimental results verify the correctness of the analysis results.(3)In order to improve the overall efficiency and performance of the system,this paper also studies the bipartite consensus of matrix-weighted multi-agent systems with leading agents.First,the leader-follow bipartit control protocol is proposed,which is studied in undirected and directed communication topologies.On the premise of ensuring the structural balance,the relevant conditions for realizing the leader-following bipartite consensus of matrix-weighted multi-agent systems are derived by using Lyapunov stability theory.Finally,MATLAB is also used for simulation verification.更多还原