随机多智能体系统稳定性综述

随机多智能体系统一致稳定性分析大致可区分为: 带随机噪声的多智能体系统的一致稳定性分析, 切换拓扑下随机多智能体系统一致稳定性分析, 随机时滞多智能体系统一致稳定性分析, 随机多智能体系统分布式优化控制一致稳定性分析. 对此, 从以上4 个方面对随机多智能体系统稳定性问题的研究进展及其存在的问题进行阐述, 并对随机多智能体系统一致稳定性的进一步研究方向进行了展望.

     

具有多时变时滞的多智能体系统在切换拓扑下的平均一致性

研究带有多时变时滞的二阶多智能体系统在切换拓扑下的平均一致性问题. 利用模型变换的方法和 Lyapunov-Krasovskii 理论, 以线性矩阵不等式(LMIs) 的形式给出了多智能体系统达到平均一致性的充分条件, 其通 讯拓扑图为联合连通的. 仿真结果验证了理论分析的正确性.

     

具有时滞和时变系数的离散多智能体系统的一致性

研究一类具有时滞和时变系数的离散多智能体系统的一致性问题. 首先, 通过构造合适的控制协议, 并以第一个智能体的位移作为参考状态, 将原系统的一致性问题转化为误差系统中零解的渐近稳定性问题; 然后, 运用矩阵范数理论研究误差系统零解的渐近稳定性, 导出使多智能体系统实现一致的充分条件; 最后, 通过数值模拟验证了该判据的正确性和有效性.

     

分布式离散多智能体系统在固定和切换拓扑下的编队控制

研究多智能体系统在分布式采样控制下固定拓扑和时变通信拓扑时的追踪和编队问题. 首先分析目标系统 在没有输入时的稳定性; 然后分别给出在固定和时变通信拓扑下使各智能体完成追踪和编队的控制协议, 并给出了系统稳定时采样间隔需满足条件的充分性和必要性证明; 最后通过仿真研究验证了所提出算法的有效性.

     

基于预测控制的时滞多机器人编队脉冲控制

针对多机器人编队控制的时滞问题, 提出一种基于预测控制的脉冲控制方法. 首先, 利用一致性思想将多机器人编队控制转换为系统稳定性问题; 然后构建预测模型, 采用脉冲控制协议, 利用Schur 稳定性定理推导实现多机器人编队控制的充分条件; 最后, 在数值仿真中随机设置一种包含生成树的通信拓扑关系, 并比较了不同采样时间间隔下时滞系统的控制效果. 仿真结果验证了所提出方法的有效性.

     

时变时滞连续切换奇异系统的一致有限时间稳定分析

讨论一类含有时变时滞的连续时间切换奇异系统的一致有限时间稳定、有限时间有界和状态反馈镇定问题. 在给定任意的切换规则下, 运用多Lyapunov 函数和平均驻留时间方法设计使得闭环系统一致有限时间稳定和有限时间有界的状态反馈控制器, 同时给出基于线性矩阵不等式表示的控制器存在的充分条件. 最后通过数值算例表明了所提出方法的合理性和有效性.

     

多图通信拓扑下一致性系统的鲁棒性度量

研究在外界扰动影响下的通信拓扑为多图的一阶多智能体系统的协同一致性控制鲁棒性问题. 采用闭环系统的??₂ 范数来度量系统的鲁棒性; 借助代数图论、控制论和矩阵论, 建立通信拓扑在有无自环时多智能体系统鲁棒性、系统??₂ 范数、系统通信拓扑之间的直接联系, 并进行严格的证明; 给出通信拓扑为完备图、星图、路图、环图时多智能体系统之间的收敛速度、鲁棒性分析与比较. 仿真实例表明了所提出方法的有效性.

     

受干预多智能体系统的一致性分析及控制

运用图论、矩阵分析和极限理论, 研究当通信拓扑结构连通的多智能体系统受到干预时, 系统仍保持一致性的充分条件及其平衡状态. 利用指数函数快速递减且可积的特性, 设计干预控制器, 控制多智能体系统收敛到指定位置. 仿真研究实验验证了所提出结论的正确性.

     

多智能体时滞和无时滞网络的加权分组一致性分析

针对连通二部图结构下的一阶多智能体系统, 考虑有无时滞两种情形下多智能体的加权分组一致问题. 设计一类基于竞争关系的分散协调控制协议, 利用矩阵论和代数图论等有利工具, 使得在该控制协议下, 多智能体系统均可全局收敛到任意指定的加权一致状态. 针对系统存在时滞的情形, 运用圆盘定理和广义奈氏准则, 得到系统达到收敛时可能容忍的最大时延上界. 仿真实例较好地验证了所得出结论的正确性.

     

时变概率随机拓扑条件下高阶群系统一致性分析

在时变连接概率的随机拓扑条件下, 研究了离散时间高阶线性群系统的一致性问题. 首先, 给出一个依赖于相邻主体间拓扑连接概率和各个主体自身信息的随机控制协议; 然后, 应用状态空间分解法分析离散时间高阶线性群系统的一致性, 给出了在连接概率时变的随机拓扑条件下以概率为1 实现一致的充分必要条件; 进而, 确定了随机拓扑条件下离散时间高阶线性群系统的一致函数; 最后, 通过数值分析验证了所得出结论的正确性.

     

离散时间多智能体系统一致性的平均驻留时间条件

研究高阶离散时间线性多智能体系统在有向切换信息拓扑下的状态一致性问题。首先通过提出的线性变换将该一致性问题转换为相应离散时间线性切换系统的渐近稳定性问题。然后借助于切换系统稳定性的平均驻留时间方法,分别得到如下两种情形下该一致性问题可解的充分条件：1)信息拓扑集合中的一部分拓扑是可一致的;2)信息拓扑集合中所有信息拓扑是可一致的。最后通过数值仿真验证了所得理论结果的正确性。     

Allowable delay bound for consensus of linear multi-agent systems with communication delay

This paper studies the consensus of a group of linear dynamic agents with a uniform communication delay and focuses on searching an allowable delay bound. As long as the delay is less than this bound, there exist linear feedback consensus protocols driving the multi-agent system to achieve consensus. Both fixed and switching topology cases are investigated. In both cases, the consensus problem is converted to the robust stability problem of corresponding uncertain state-delayed systems. By using Lyapunov–Krasovskii functional analysis, consensus conditions which contain the feedback gain conditions and delay conditions are proposed for systems over fixed and switching topologies, respectively. Furthermore, allowable delay bounds are obtained for both systems by solving the optimal robust stabilisation problems. Numerical examples are given to illustrate the results.     

切换信息拓扑和时变时滞下离散时间线性多智能体系统一致性的平均驻留时间条件（英文）

This paper investigates the consensus problem of discrete-time linear multi-agent systems(DLMASs) with directed switching information topologies and time-varying delays. First, we transform the consensus problem to an asymptotic stability problem of a corresponding time-delayed switched linear system(TDSLS) via a proper linear transformation. Then by using a constructed Lyapunov functional and the average dwell-time scheme, we establish a novel delay-dependent sufficient condition for the solvability of the consensus problem in terms of linear matrix inequalities(LMIs) for two cases, respectively: 1) all of the given information topologies are consensusable; 2) some of the given information topologies are consensusable. Finally, numerical examples are given to show the validness of the established results.     

切换信息拓扑和时变时滞下离散时间线性多智能体系统一致性的平均驻留时间条件

研究了有向切换信息拓扑和时变时滞下离散时间线性多智能体系统的一致性问题.首先,通过适当的线性变换把一致性问题转化为相应的时变时滞线性切换系统的渐近稳定问题; 然后,利用构建的李亚普诺夫函数和平均驻留时间模式,建立了一致性问题可解的基于线性矩阵不等式的时滞依赖充分条件,研究了如下两种情形: 1)所有信息拓扑都是可一致的,2) 部分信息拓扑是可一致的; 最后,数值实例验证了结果的正确性.     

时延异构多自主体系统的群一致性分析

针对由一阶自主体和二阶自主体构成的异构多自主体系统的静态群一致性问题,分别提出了在固定连接拓扑和切换连接拓扑结构下的静态群一致性算法。通过构造Lyapunov-Krasovskii函数,得到了系统在具有相同时变通信时延的群一致性算法作用下渐近收敛群一致的充分条件,并以线性矩阵不等式表示。最后,仿真结果表明,所提算法在满足一定条件下能使时延异构多自主体系统渐近收敛群一致。     

Distributed adaptive consensus for multiple mechanical systems with switching topologies and time-varying delay

This paper studies the adaptive consensus problem of networked mechanical systems with time-varying delay and jointly-connected topologies. Two different consensus protocols are proposed. First, we present an adaptive consensus protocol for the connected switching topologies. Based on graph theory, Lyapunov stability theory and switching control theory, the stability of the proposed algorithm is demonstrated. Then we investigate the problem under the more general jointly-connected topologies, and with concurrent time-varying communication delay. The proposed consensus protocol consists of two parts: one is for the connected agents which contains the current states disagreement among them and the other is designed for the isolated agents which contains the states difference between the current and past. A distinctive feature of this work is to address the consensus control problem of mechanical systems with unknown parameters, time-varying delay and switching topologies in a unified theoretical framework. Numerical simulation is provided to demonstrate the effectiveness of the obtained results.     

Asynchronous decentralised event-triggered control of multi-agent systems

In this paper, the consensus problem of first-order multi-agent systems under linear asynchronous decentralised event-triggered control is investigated. Both undirected and directed topologies are considered. In the analysis, the closed-loop multi-agent systems with the event-triggered control are modelled as switched systems. After proposing the decentralised event-triggered consensus protocols, decentralised state-dependent event conditions are derived, which act as switching signals. The consensus analyses are performed based on graph theory and stability results of switched systems. Under the event-triggered control schemes presented, consensus is reached with enlarged sampling periods and no Zeno behaviour. Simulation examples are given to illustrate the effectiveness of the proposed theoretical results.     

Distributed consensus of multi‐agent systems with general linear node dynamics and intermittent communications

Without assuming that the mobile agents can communicate with their neighbors all the time, the consensus problem of multi‐agent systems with general linear node dynamics and a fixed directed topology is investigated. To achieve consensus, a new class of distributed protocols designed based only on the intermittent relative information are presented. By using tools from matrix analysis and switching systems theory, it is theoretically shown that the consensus in multi‐agent systems with a periodic intermittent communication and directed topology containing a spanning tree can be cast into the stability of a set of low‐dimensional switching systems. It is proved that there exists a protocol guaranteeing consensus if each agent is stabilizable and the communication rate is larger than a threshold value. Furthermore, a multi‐step intermittent consensus protocol design procedure is provided. The consensus algorithm is then extended to solve the formation control problem of linear multi‐agent systems with intermittent communication constraints as well as the consensus tracking problem with switching directed topologies. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.