基于滑模的二阶多智能体快速抗扰一致性

针对带有外部未知扰动的二阶多智能体系统的领导—跟随有限时间一致性问题，本文设计出一种带有时变增益的有限时间干扰观测器，用以实现对每个跟随智能体中未知扰动的快速估计，在此基础上，本文结合超螺旋积分滑模控制方法并利用邻居智能体的位置和速度信息设计一种快速抗扰一致性协议，该协议能够保证存在非线性动态的多智能体系统有限时间一致性控制并能抑制抖振现象.同时，利用李亚普诺夫函数进行了稳定性的证明.最后，通过Matlab数值仿真进一步验证了所提出协议的可行性.     

2阶多智能体网络在切换拓扑下的群一致性

针对2阶多智能体网络的群一致性问题,提出了基于牵引控制方法的群一致性协议.考虑到网络模型具有切换拓扑结构,在模型中引入相应的虚拟领导者.对于网络中的每一个智能体,其一致性协议依赖于智能体邻居的状态及速度信息,并受到虚拟领导者的牵引控制;进一步地,来自虚拟领导者的牵引控制可以随时间发生变换.利用代数图论、线性矩阵不等式和李亚普诺夫稳定性理论,对网络进行群一致性分析,给出了切换拓扑下2阶多智能体网络达到群一致性的充分条件.最后,数值仿真验证了理论结果的有效性.     

一类离散时间切换系统鲁棒控制器设计

考虑一类非线性离散时间切换系统的鲁棒二次镇定和渐近镇定问题．利用公共李亚普诺夫函数方法和多李亚普诺夫函数方法，分别设计了切换系统鲁棒状态反馈控制器和输出反馈控制器，保证了切换系统的二次稳定性和渐近稳定性．仿真结果验证了所提出算法的有效性．     

不确定离散时滞分段系统的广义H2弹性控制

针对一类不确定离散时滞分段系统,研究了广义H2稳定性分析和带有时滞的状态反馈弹性控制器设计问题.通过构造适当的离散分段二次李亚普诺夫函数,利用分段二次李亚普诺夫稳定性理论,给出了对于所有的容许参数不确定性,闭环系统是广义H2稳定的充分条件;在此基础上,基于线性矩阵不等式(LMI)处理方法,提出了带有时滞的状态反馈弹性控制器增益阵的设计方案.仿真实例验证了所提方法的有效性.     

一类非完整轮式机器人的编队一致性

讨论了一类具有非完整约束和有向通信拓扑的轮式机器人的编队一致性问题.基于Zipf分布设计了带有耦合权重的编队一致性协议,减少了机器人间的信息交换,降低机器人编队在复杂的通讯环境中对所有机器人状态信息的依赖程度.将多机器人系统的编队一致性问题转化为误差系统的稳定性分析问题,给出了机器人形成编队的一致性条件,并利用图论和李亚诺夫稳定性理论证明在该条件下可实现系统编队收敛到期望的队形和虚拟领导者的运动规律上的目标.仿真实验和实物实验验证了所设计编队一致性协议的有效性.     

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.     

不确定时变时滞多个体系统的鲁棒H∞一致性控制

在多时变时滞的固定无向拓扑结构下,考虑了带有干扰和不确定性的多个体系统的鲁棒H∞一致性问题.首先,将多个体系统的一致性问题转化为低维多个体系统的一致性问题;然后针对低维系统构建李亚普诺夫函数,给出了多个体系统一致性问题的鲁棒线性H∞反馈控制律存在的充分条件,并利用线性矩阵不等式表示.Matlab 仿真验证了本文所给控制方法的有效性.     

李亚普诺夫方法的发展与历史性成就——纪念李亚普诺夫的博士论文“运动稳定性的一般问题”发表一百周年

本文论述了李亚普诺夫方法的发展,全文共分七部分:1 李亚普诺夫方法产生的历史背景;2 在李亚普诺夫原数学模式中的发展;3 在反馈系统中的发展与应用;4 李亚普诺夫方法与时变、不确定系统;5 在理论上的进一步发展;6 比较原理与李亚普诺夫方法;7 结束语。     

混沌系统的自适应函数投影同步与参数辨识

为了实现两未知参数混沌系统的同步控制与参数辨识,采用自适应函数投影同步控制策略,基于李亚普诺夫稳定性原理,设计了实现参数未知、不同初值的两同构或异构混沌系统同步的控制器和参数自适应控制律,给出了实现同步的控制参数的取值范围,分析了控制参数对同步系统性能的影响规律.以最新提出的单参数简化洛仑兹混沌系统模型为研究对象,采用Matlab/Simulink进行动态仿真研究,表明了理论分析的正确性和同步控制与参数辨识方法的有效性.     

不确定多重状态时滞离散系统的LMI鲁棒稳定条件

研究了具有多重状态时滞的凸多面体不确定离散系统的鲁棒稳定性分析问题．基于参数依赖的李亚普诺夫稳定性和线性矩阵不等式推导出使得时滞鲁棒稳定系统鲁棒稳定的充分条件．应用此条件，通过测试一组线性矩阵不等式的可解性即可达到判定系统的鲁棒稳定性的目的．因为使用了参数依赖的李亚普诺夫稳定性思想，此鲁棒稳定条件比基于二次稳定概念的稳定条件的保守性更小．算例验证了结果．     

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.     

异质多智能体系统滞后一致性跟踪控制

针对一阶、二阶混合异质多智能体系统的滞后一致性问题,提出了一种基于牵制控制的分布式滞后一致性控制协议。首先,将滞后一致性分析转化为稳定性证明;然后,利用图论和Lyapunov稳定性理论分析闭环系统稳定性;最后,分别在固定拓扑和切换拓扑结构下给出了基于线性矩阵不等式（LMI）形式的滞后一致性可解的充分条件,从而实现异质多智能体的领导-跟随者滞后一致性。数值仿真结果表明,所提出的滞后一致性控制方法可以使异质多智能体系统实现领导-跟随者滞后一致性。     

Consensus with guaranteed convergence rate of high-order integrator agents in the presence of time-varying delays

This paper aims to study the consensus problem in directed networks of agents with high-order integrator dynamics and fixed topology. It is considered the existence of non-uniform time-varying delays in the agents control laws for each interaction between agents and their neighbours. Based on Lyapunov–Krasovskii stability theory and algebraic graph theory, sufficient conditions, in terms of linear matrix inequalities, are given to verify if consensus is achieved with guaranteed exponential convergence rate. The efficiency of the proposed method is verified by numerical simulations. The simulations reveal that the conditions established in this work outperformed the similar existing ones in all numerical tests accomplished in this paper.     

Event‐triggered Control for Cluster Consensus in Multi‐agent Networks

This paper considers the issue of cluster consensus for multiple agents in fixed and undirected networks. Agents in a network are supposed to split into several clusters, and a fraction of the agents in each cluster are pinned by virtual leaders. According to the Lyapunov stability theory and graph theory, some appropriate event‐triggered protocols are developed for consensus of the agents belonging to the same cluster, which can greatly reduce both the number of communication updates and that of control actuation updates. Finally, a numerical example is shown to demonstrate the effectiveness of the proposed theoretical results.     

输入与速度饱和的异构多智能体系统的一致性

针对由一阶与二阶智能体构成的异构多智能体系统具有输入和速度饱和特性,系统无法达到一致性的问题,构建了无领航者和有领航者的异构多智能体分布式控制器,并给出了系统达到一致性的充分条件。通过Lyapunov稳定性理论和Lasalle不变集原理推导出了系统稳定性的充分条件,并以此计算出了通信增益的取值范围。对具有输入和速度饱和特性的无领航者异构多智能体系统进行数值仿真,结果显示,当选取的通信增益不在合适的范围内时,无领航者的异构多智能体系统无法实现一致性;而通过提出的增益选取方法选取通信增益时,异构多智能体系统可以克服输入和速度的饱和特性,进而实现异构多智能体系统的半全局一致性。对具有输入和速度饱和特性的领航跟随异构多智能体系统进行数值仿真的结果则证明了通信增益的计算方法也适用于异构多智能体系统的半全局领航跟随一致性控制。     

Adaptive finite-time consensus in multi-agent networks

This paper is concerned with the finite-time consensus problem of distributed agents having non-identical unknown nonlinear dynamics, to a leader agent that also has unknown nonlinear control input signal. By parameterization of unknown nonlinear dynamics, a Lyapunov technique in conjunction with homogeneity technique is presented for designing a decentralized adaptive finite-time consensus control protocol in undirected networks. Homogeneous Lyapunov functions and homogeneous vector fields are introduced in the stability analysis although the whole system is not homogeneous. Theoretical analysis shows that leader-following consensus can be achieved in finite-time, meanwhile, finite-time parameter convergence can be also guaranteed under the proposed control scheme. An example is given to validate the theoretical results.     

Error-transformation-based consensus algorithms of multi-agent systems: connectivity-preserving approach

This paper investigates distributed connectivity-preserving consensus problems of networked multi-agent systems with limited communication ranges. Compared with existing literature, a main contribution of this paper is to present a new nonlinear transformation approach of consensus errors for preserving the initial interaction patterns of multi-agent systems. Both the consensus and the connectivity preservation can be achieved by using one transformed error function. Based on the proposed nonlinear error transformation, we derive distributed connectivity-preserving consensus algorithms for single-integrator dynamics, double-integrator dynamics and second-order nonlinear systems. The asymptotic stability of consensus errors and the connectivity preservation among agents are established through Lyapunov stability analysis.     

Absolute stability analysis of discrete-time systems with composite quadratic Lyapunov functions

A generalized sector bounded by piecewise linear functions was introduced in a previous paper for the purpose of reducing conservatism in absolute stability analysis of systems with nonlinearity and/or uncertainty. This paper will further enhance absolute stability analysis by using the composite quadratic Lyapunov function whose level set is the convex hull of a family of ellipsoids. The absolute stability analysis will be approached by characterizing absolutely contractively invariant (ACI) level sets of the composite quadratic Lyapunov functions. This objective will be achieved through three steps. The first step transforms the problem of absolute stability analysis into one of stability analysis for an array of saturated linear systems. The second step establishes stability conditions for linear difference inclusions and then for saturated linear systems. The third step assembles all the conditions of stability for an array of saturated linear systems into a condition of absolute stability. Based on the conditions for absolute stability, optimization problems are formulated for the estimation of the stability region. Numerical examples demonstrate that stability analysis results based on composite quadratic Lyapunov functions improve significantly on what can be achieved with quadratic Lyapunov functions.     

Finite-time consensus control for second-order multi-agent systems without velocity measurements

This paper investigates the finite-time consensus problem for second-order multi-agent systems with unknown velocities and disturbances. By introducing the second-order sliding mode observer, two novel distributed finite-time protocols with only relative position measurements are proposed for the both cases with known and unknown boundaries of disturbances. On the basis of Lyapunov stability theorem and homogeneous theory, it is proved that the consensus can be achieved in finite time. Simulation examples are provided to show the effectiveness of the theoretical results.     

一类异质多智能体系统的一致性控制

针对一类由连续时间一阶和二阶智能体组成的异质多智能体系统,首先给出一阶和二阶智能体实现一致性的算法,其次利用图论和矩阵理论相关知识,在固定有向拓扑结构下,给出异质多智能体系统实现一致性的充要条件,且在一致性实现时给出一致性状态的确切表达式;在切换拓扑结构下,给出异质多智能体系统实现一致性的充分条件。最后给出数值算例验证了相关结论的有效性。