基于模型简化法的多时延多智能体H_∞一致性研究

Research on the H_∞ Consensus Problem of Multi-agent Systems with Multiple Input Delays Based on Model Reduction

为了解决线性多智能体系统的H_∞一致性问题,针对多智能体系统存在干扰且含有多个输入时延的有向网络提出一致性协议,并对该协议进行理论分析。通过模型简化法与Lyapunov泛函法对连接拓扑图的邻接矩阵及拉普拉斯矩阵进行数据分析,并寻找一种控制器使该系统达到H_∞一致性。在此基础上,为了满足含有多个时延的线性多智能体系统模型H_∞的一致性,设计控制器参数与系统内部参数之间的数学关系。最后对某个含有多个输入时延的多智能体系统进行MATLAB仿真分析,验证了该一致性控制协议的有效性与普遍性。

The main purpose of this paper is to study the consistency of linear multi-agent systems.In this paper,a consistent protocol is proposed for a multi-agent system with interference and multiple input delays in a directed network,and a theoretical analysis of the protocol is made.The adjacency matrix of the connection topology is analyzed by the model reduction method and the Lyapunov functional method.Laplacian matrix is used for data analysis and a controller is found to make the system consistent.On this basis,this paper also finds out the mathematical relationship between the controller parameters and the internal parameters of the system to satisfy the consistency of the linear multi-agent system model with multiple delays.Finally,a MATLAB numerical simulation is used to simulate a multi-agent system with multiple input delays,and the validity and universality of the conformance control protocol are verified.