线性多智能体系统的一致性与能控性分析

项目名称： 线性多智能体系统的一致性与能控性分析

项目编号： No.61304163

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 自动化技术、计算机技术

项目作者： 蒋方翠

作者单位： 山东大学

项目金额： 22万元

中文摘要： 由于在机器人编队控制、传感器网络数据融合等领域的广泛应用，多智能体系统的一致性理论已经成为了一个热门的研究课题。本项目采用控制理论、代数图论、矩阵理论、稳定性理论等理论工具，研究线性控制多智能体系统的一致性和基于一致性协议的能控性，并力求理论结果在强迫一致性、pinning控制中的应用。首先基于Lyapunov方程为线性控制多智能体系统的一致性建立网络拓扑依赖性弱的协议参数设计，使得所有智能体状态最终到达某静态一致性状态。其次，依据有无外界控制输入将智能体分为领航者与跟随者，在所给出的一致性协议下建立线性控制多智能体系统能控性分析的数学模型，给出系统完全能控的图论描述条件。最后，基于能控性分析的数学模型和最优化方法，给出最优领航者的选取及最优通信加权的设计。本项研究不仅能够促进一致性理论的发展、深入揭示一致性协议的作用机理，而且能够为多智能体支撑系统的协调控制等应用领域提供重要的理论依据。

中文关键词： 线性多智能体系统；一致性；时滞；脉冲控制；能控性

英文摘要： Because of the wide applications in the formation control of robots, data fusion of sensor networks, etc, the consensus theory of multi-agent systems has been an active research subject. By applying control theory, algebraic graph theory, matrix theory, stability theory etc,this project studies the consensus of linear control multi-agent systems and the controllability based on consensus protocols, and strives for the applications of theoretical results in forced consensus and pinning control. Based on Lyapunov equation, the project first establishes a design for protocol parameters which has weak dependence on the network topology. Under the design of consensus protocol, the states of all the agents reach to a static consensus state eventually. Second, according to whether there exists exogenous control input or not, we partition all the agents into leaders and followers. Under given consensus protocols , we build the mathematical models for the controllability analysis of linear control multi-agent systems, and provide graph-theoretic conditions for the complete controllability of the systems. Finally, on the base of the mathematical models of controllability analysis and the optimization methods, we present the optimal election of leaders and the optimal design of communication weights. The study of this proj

英文关键词： linear multi-agent systems；consensus；time-delays；impulsive control；controllability