具有时延的多个体系统的一致性问题综述

考察了具有时延的多个体系统的一致性问题．根据不同的分析方法,介绍了关于具有通信时延的多个体系统一致性问题的结果,并对各种分析方法的特点进行了比较．此外,对具有输入时延的多个体系统的现有一致性结果也作了介绍．最后评述了该研究领域存在的问题以及今后的研究方向．

     

时延多智能体系统领导跟随一致性研究

为符合实际情形,针对不确定与随机发生非线性的多智能体系统,研究了有时延且网络拓扑切换时系统的领导跟随一致性。传统协议通常保守的假设邻接个体间通信时延与个体和领导者间通信时延大小相同,新协议中上述时延可以大小不同。相比于传统方法,新颖的将复杂网络同步问题研究领域对时延的处理方法引入到多智能体系统一致性问题的研究中,利用一类推广的Halanay不等式,给出系统实现领导跟随一致性需满足的两个与时延无关的充分条件,即时延在相关参数满足定理条件的前提下不影响系统最终实现一致性。相比其他方法得到的含有时延的判定条件,本研究结果保守性更低,实例仿真验证了新协议的可行性。     

具有通信时延和输入时延的1阶多自主体系统的一致性问题

研究了同时具有时变通信时延和定常输入时延的1阶多自主体系统的一致性问题.假设多自主体系统的连接拓扑中各节点的输出度相等,采用变量代换将原多自主体系统的一致性问题转化为降阶系统的渐近稳定性问题.根据李亚普诺夫渐近稳定性定理以及线性矩阵不等式法,在通信时延导数信息已知和未知的情况下,分别得到了多自主体系统在静态和连通拓扑结构下渐近一致的充分条件,且该条件与通信时延和输入时延都相关.仿真结果验证了结论的有效性.     

具有通信时延的离散时间二阶多个体网络的一致性问题

针对具有通信时延的离散时间二阶多个体系统的一致性问题,采用了具有静态领导者的一致性算法.根据广义Nyquist判据和Gerschgorin圆盘定理,得到了系统渐近收敛到领导者状态的充分条件.在个体与领导者构成的连接拓扑满足一定连通性的前提下,该充分条件是分散形式的,与控制参数、邻居个体之间的连接权值相关,而与通信时延大小无关.仿真结果证明了结论的正确性.     

离散时间分数阶多自主体系统的时延一致性

复杂工作环境中,许多自然现象的个体动力学特性用整数阶方程不能描述,只能用非整数阶（分数阶）动力学来描述个体的运动行为. 本文假设多自主体系统内部连接组成有向加权网络,个体的动态特性应用分数阶动力学方程描述,个体之间数据传输存在通信时延. 应用分数阶系统的Laplace变换和频域理论,研究了离散时间的分数阶多自主体系统的渐近一致性. 应用Hermit-Biehler 定理,研究了具有样本时延的分数阶多自主体系统的运动一致性,得到保证系统稳定的时延的上界阈值. 最后应用一个实例对结论进行了验证.     

通信时延下多智能体系统的安全一致性控制

研究了离散时间多智能体系统存在通信时延条件下的安全一致性问题.本文的目标是设计一种一致性控制算法能够使得网络中各正常智能体抵御敌对智能体的攻击并实现最终状态一致.该算法仅利用个体的自身状态和相邻个体的时延信息作为控制输入,并根据控制器参数、拓扑属性和通信时延,获得了所提算法实现收敛的充要条件.最后,通过仿真实例对理论结果进行了验证.     

异构变时延多智能体系统编队控制分析

实际工程应用中,异构多智能体的编队控制问题研究具有十分重要的意义。考虑现实环境影响,编队系统个体之间的通信变时延难以忽略。系统收敛速率是评价系统性能的重要依据,然而现有编队控制问题研究很少能给出相应的量化指标。针对上述情形,对包含一、二阶智能体的异构变时延系统的编队控制问题进行分析研究。首先,考虑固定有向通信拓扑情况,对领航跟随者模式下异构变时延多智能体系统提出线性一致性控制协议。然后,构建误差系统模型,利用图论与矩阵论分析方法,并结合Routh-Hurwitz定理与牛顿-莱布尼兹公式,获得系统实现编队控制的充要条件,同时得到估算系统收敛速率的不等式关系。最后,仿真算例中随机给定一种系统节点0全局可达的通信拓扑,并对不同时延情况的编队控制效果进行分析,验证一致性控制协议的正确性和有效性。     

具有随机时延的的多智能体系统的一致性

本文研究了具有随机时不变通信时延的多智能体系统的一致性问题。假设系统拓扑是固定有向的强连通图,考虑多智能体系统中存在随机通信时延的情况,即各智能体之间的通信时延是以一定概率存在的,采用具有动态参考状态的一致性控制算法,通过变量代换,将多智能体的一致性问题转化为误差系统的渐进稳定性问题,然后再应用Lyapunov稳定性理论与随机分析方法推导出误差系统在该算法作用下趋于稳定的充分条件,并以线性矩阵不等式（LMIs）表示,即原多智能体系统在此充分条件下各智能体的状态能够达到一致。最后应用一个实例验证了所提出结论的有效性。     

具有随机通信时延的二阶多智能体系统的一致性控制

研究了具有随机通信时延的二阶多智能体系统的一致性控制问题.分别讨论了具有固定拓扑结构和变化拓扑结构两种情形下二阶多智能体系统在具有随机通信时延情况下的一致性问题.通过构造Lyapunov函数的方法得到多智能体系统的时延依赖稳定判据,并以线性矩阵不等式(LMI)的形式给出了系统稳定的条件.最后,仿真和实验结果验证了研究所得结论的正确性和有效性.     

具有通信时延的二阶多智能体系统有限时间一致性跟踪控制

针对具有通信时延的二阶多智能体系统的有限时间一致性控制问题,分别研究了具有固定拓扑和切换拓扑网络结构情形下的二阶多智能体系统的有限时间一致性。为使多智能体系统能在有限时间内可以达到一致,引入一致性控制增益矩阵并设计了相应的基于相对位置和相对速度的时延状态误差有限时间一致性控制算法,利用系统模型转换,泛函微分方程稳定性理论和有限时间Lyapunov稳定性定理得到了使系统在有限时间内达到一致跟踪的最大时延上界值。最后,仿真实验结果验证了所得理论的正确性和有效性。     

Consensus problem of heterogeneous multi-agent systems with time delay under fixed and switching topologies

Consensus problem is investigated for heterogeneous multi-agent systems composed of first-order agents and second-order agents in this paper. Leader-following consensus protocol is adopted to solve consensus problem of heterogeneous multi-agent systems with time-varying communication and input delays. By constructing Lyapunov-Krasovkii functional, sufficient consensus conditions in linear matrix inequality(LMI) form are obtained for the system under fixed interconnection topology. Moreover, consensus conditions are also obtained for the heterogeneous systems under switching topologies with time delays. Simulation examples are given to illustrate effectiveness of the results.     

具有时滞的混合阶多智能体系统的组一致性

针对由离散时间一阶和二阶智能体组成的混合阶多智能体系统,研究其在固定和切换拓扑结构下受通信时滞影响时的组一致性问题。分别为两类智能体提出组一致性协议,引入模型变换,将闭环系统转化为等价系统。在一定假设条件下,以代数图论、矩阵理论为主要研究工具,分别在固定和切换拓扑结构下给出了混合阶多智能体系统实现渐近组一致性的条件。采用数值仿真对所得结果的有效性进行了验证。     

Guaranteed Cost Consensus for High-dimensional Multi-agent Systems With Time-varying Delays

Guaranteed cost consensus analysis and design problems for high-dimensional multi-agent systems with timevarying delays are investigated. The idea of guaranteed cost control is introduced into consensus problems for high-dimensional multi-agent systems with time-varying delays, where a cost function is defined based on state errors among neighboring agents and control inputs of all the agents. By the state space decomposition approach and the linear matrix inequality (LMI), sufficient conditions for guaranteed cost consensus and consensualization are given. Moreover, a guaranteed cost upper bound of the cost function is determined. It should be mentioned that these LMI criteria are dependent on the change rate of time delays and the maximum time delay, the guaranteed cost upper bound is only dependent on the maximum time delay but independent of the Laplacian matrix. Finally, numerical simulations are given to demonstrate theoretical results.      

Consensus of second-order multi-agent systems with nonlinear dynamics and time delays

In this paper, consensus problems of multi-agent systems with nonlinear dynamics and time delays are investigated. Two cases are considered that are the system without a leader and the one with a leader. New linear control protocols are introduced to make second-order multi-agent systems consensus. By applying the Lyapunov function method and the graph theory, some sufficient conditions for consensus of positions and velocities are derived. Finally, two simulation results are given to illustrate the effectiveness of our proposed methods.     

Necessary and sufficient condition for average consensus of networked multi-agent systems with heterogeneous time delays

This paper deals with an average-consensus problem of networked multi-agent systems with heterogeneous time delays. First, a necessary and sufficient condition is derived for multi-agent systems to achieve average consensus. This condition is represented in the form of an algebraic condition by using the delay-transition and the delay-weighted Laplacians. Second, a performance criterion is introduced to evaluate multi-agent systems that do not achieve average consensus. The criterion is represented in terms of the norms with respect to the above Laplacians. These results imply that the introduced Laplacians play important roles in analysing multi-agent systems with heterogeneous time delays. The validity of the analysis results is demonstrated by simulations with six-agent systems.     

Necessary and sufficient conditions for mean square consensus under Markov switching topologies

This article deals with the mean square consensus problem for second-order discrete-time multi-agent systems. Both cases of systems with and without time delays in Markov switching topologies are considered. With the introduced control protocols, necessary and sufficient conditions for mean square consensus of second-order multi-agent systems are derived. Under the given control protocols in Markov switching topologies, the second-order multi-agent systems can reach mean square consensus if and only if each union of the graphs corresponding to all the nodes in closed sets has a spanning tree. Finally, a simulation example is provided to illustrate the effectiveness of our theoretical results.     

Mean square average-consensus for multi-agent systems with measurement noise and time delay

Mean square average consensus for multi-agent systems with measurement noise and time delay under fixed digraph is studied in this article. The time-varying consensus-gain is introduced to attenuate the measurement noise. By combining the tools of algebraic graph theory, matrix theory and stochastic analysis, consensus protocols for multi-agent systems with measurement noise and time delay are elaborately analysed. The example and simulation results are given to illustrate the effectiveness of the obtained theoretical results. Moreover, the simulations demonstrate that, the proper consensus-gain function in the consensus protocol is the necessary and sufficient condition for the convergence of the multi-agent systems.     

具有时延和切换拓扑的高阶离散时间多智能体系统鲁棒保性能一致性

研究存在参数不确定性的高阶离散时间多智能体系统在时延和联合连通切换通信拓扑条件下的鲁棒保性能一致性问题,给出一种线性一致性协议的设计方法.1）引入高阶离散时间不确定多智能体系统的鲁棒保性能一致性问题,定义基于智能体邻居状态误差和控制输入的保性能函数;2）通过构造合适的Lyapunov函数并利用离散时间系统稳定性理论,推导出一个使高阶离散时间不确定多智能体系统在该条件下获得保性能一致性的线性矩阵不等式（Linear matrix inequality,LMI）充分条件,并给出相应的保性能上界;3）以一致性序列的形式给出参数不确定条件下的高阶离散时间多智能体系统的一致性收敛结果;4）数值仿真验证了本文理论的正确性和有效性.     

多自主体量化趋同与有限数据率趋同综述

对近年来系统控制学科的一个前沿热点领域——多自主体系统的量化趋同和有限数据率趋同问题进行了回顾和总结. 介绍了该领域产生和发展的背景及意义; 分门别类地回顾了该领域一些代表性成果和研究方法; 并结合多自主体系统和网络化控制的大背景,对该领域未来可能的研究方向进行了展望.     

A new framework for consensus for discrete-time directed networks of multi-agents with distributed delays

In this article, the distributed consensus problem is considered for discrete-time delayed networks of dynamic agents with fixed topologies, where the networks under investigation are directed and the time delays involved are distributed time delays including a single or multiple time delay(s) as special cases. By using the invariance principle of delay difference systems, a new unified framework is established to deal with the consensus for the discrete-time delayed multi-agent system. It is shown that the addressed discrete-time network with arbitrary distributed time delays reaches consensus provided that it is strongly connected. A numerical example is presented to illustrate the proposed methods.