基于状态反馈和输出反馈的离散线性多智能体系统的二分一致性研究  

Bipartite state consensus of discrete-time linear multi-agent systems via state feedback and output feedback

作　　者：姚瑶 张捷 王健安[1,2] 李晓磊 李志强 YAO Yao;ZHANG Jie;WANG Jian-an;LI Xiao-lei;LI Zhi-qiang(School of Electronics Information Engineering,Taiyuan University of Science and Technology,Taiyuan 030024,China;Shanxi Key Laboratory of Advanced Control and Equipment Intelligence,Taiyuan 030024,China;School of Electrical Engineering,Yanshan University,Qinhuangdao 066004,China;The 32nd Research Institute of China Electronics Technology Group Corporation,Shanghai 201808,China)

机构地区：[1]太原科技大学电子信息工程学院,太原030024 [2]先进控制与装备智能化山西省重点实验室,太原030024 [3]燕山大学电气工程学院,河北秦皇岛066004 [4]中国电子科技集团公司第三十二研究所,上海201808

出　　处：《控制与决策》2025年第2期537-545,共9页Control and Decision

基　　金：山西省基础研究计划项目(202203021222186,20210302123210);太原科技大学博士科研启动基金项目(20222127);来晋工作优秀博士奖励资金项目(20222127);山西省科技创新人才团队专项计划项目(202304051001035);国家自然科学基金项目(62103352)。

摘　　要：基于状态反馈和输出反馈控制方法,解决离散线性领导-跟随多智能体系统的二分状态一致性跟踪控制问题,领导者具有离散自治动态并能够产生理想参考轨迹信号.首先,基于盖尔圆盘定理和离散代数黎卡提方程提出一种新型分布式状态反馈控制协议,基于系统拓扑矩阵设计的控制耦合增益能够使得全局跟踪误差系统包含在单位圆的稳定域内.在结构平衡条件下,通过Lyapunov稳定性理论和分离原理可证明符号有向图下两个对立子组的智能体可实现二分状态一致.然后,基于邻居合作-竞争交互信息引入新型分布式状态观测器以实现跟随者状态的跟踪,进而提出一类基于观测器的输出反馈二分控制协议,在状态不可获知情况下可实现理想的领导-跟随二分状态跟踪,也可应用于更一般的传统一致性控制场景.最后,给出两个仿真算例验证所提出算法的可行性和有效性.Based on state feedback and output feedback control methods,the bipartite state consensus tracking control problem for discrete linear leader-following multi-agent systems(MASs)is solved,where the leader has discrete autonomous dynamics and can generate ideal reference trajectory signal.Firstly,a new distributed state feedback control protocol is proposed based on the Gerschgorin circle theorem and the discrete algebraic Riccati equation.The control coupling gain based on the system topology matrix enables the global tracking error system locate in the stable region of the unit circle.Under the structurally balanced condition,it can be proved that the agents of two opposite subgroups under the signed directed graph can achieve bipartite state consensus using the Lyapunov stability theory and separation principle.Then,based on the cooperative-competitive interaction information of neighbours,a new distributed state observer is introduced to realize the tracking for the state of a follower.Furthermore,an observer-based output feedback bipartite control protocol is proposed to achieve the ideal leader-follower bipartite state tracking under the condition that the states are not known,which can also be applied to more general consensus control scenarios.Finally,two numerical examples are given to illurstrate the feasibility and effectiveness of the proposed algorithms.

关 键 词：离散动态 多智能体系统 稳定域 二分状态一致 代数黎卡提方程 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]