有向网络下线性多个体系统的整体行为—–矩阵方法

研究了有向通讯网络条件下一阶和二阶线性多个体协同动力学系统整体行为的矩阵代数性质.利用矩阵分析的方法将系统的系数矩阵变换为Frobenius标准型,由此将系统分解为独立基本子系统和非独立基本子系统的组成结构.通过研究行和为零的对角占优矩阵的性质,得出了对线性多个体协同动力学系统整体行为起决定作用的系数矩阵的性质,从而将这一问题转换为普通线性代数问题.     

有向网络下仿射非线性多个体协同动力学系统的整体行为

本文讨论有向通讯网络条件下仿射非线性多个体动力学系统的结构及其整体行为．系统可以分解为独立基本子系统和非独立基本子系统．每个独立基本子系统将趋于自身的一致状态,非独立子系统的个体状态将趋于独立基本子系统一致状态为顶点的凸集内．系统所有个体的状态趋于一致的充分必要条件是存在唯一的独立基本子系统．这一结果涵盖了线性多个体动力学系统此前的研究结果．     

两类推广的渐近迭代逼近

在计算机辅助设计领域里,曲线或曲面的渐近迭代逼近(Progressive iterative approximation,PIA)性质在插值与拟合问题中有着广泛的应用,以前的文献对这一性质的讨论主要局限在标准全正基的情形.对于一般的非标准全正基,本文指出,其在适当的参数下也有可能同样具有这一优良的性质,并给出了相应的实例,从而拓宽了渐近迭代逼近的适用范围.与此同时,还讨论了权因子各不相同时,带权渐近迭代逼近的收敛性,使得迭代逼近曲线对不同的控制顶点,具有不同的加速收敛速度.     

二阶有向多智能体网络的可控包含控制

研究随机给定拓扑结构的二阶有向多智能体网络的可控包含控制问题.针对当前包含控制研究成果大多没有考虑多智能体网络领导者和跟随者的可控配置问题,结合复杂网络可控性理论和二分图最大匹配算法给出满足网络可控的领导者和跟随者集合,并为跟随者智能体设计相应的控制协议,驱使跟随者能够渐近收敛到由多个领导者构成的静态凸包中,从而实现网络的可控包含控制.仿真结果验证了理论分析的正确性.     

有向网络下非线性多智能体系统的协调跟踪

基于一致性理论,在有向拓扑结构下研究非线性多智能体系统的协调跟踪控制问题．考虑智能体动力学模型为一般且仅满足Lipschitz条件的非线性系统,在仅有部分跟随智能体能获取领航智能体信息的情形下,当领航智能体与跟随智能体之间的拓扑结构具有有向生成树,即存在领航智能体到所有跟随智能体的有向路径时,所设计的分布式控制律可实现所有跟随智能体对领航智能体的跟踪,并指出该拓扑结构是系统实现跟踪的一个必要条件．最后,仿真实验验证了所设计控制算法的有效性．     

带有不确定时变延时的有向网络多智能体平均一致性研究

针对带有不确定时变通信延时的有向网络多智能体系统的平均一致性问题,本文首先深入分析了弱连接且平衡的固定/切换拓扑特性.然后,通过分解系统状态变量,建立了初始系统的降维综合模型.考虑降维模型带有不确定时变延时,基于Jensen's不等式和最近提出的新型互凸方法,得到了系统平均一致性的充分条件,特别是,给出了与目前研究结果相比具有更小保守性的时变通信延时上界.最后,数值仿真验证了提出方法的可行性和有效性.     

有向通讯网络下一类动态群体的整体动力学行为

本文运用图论、矩阵分析和现代控制理论的方法,研究有向通讯网络下一类二维群体的全局动力学行为.此类群体由众多具有相同动力学性质的个体组成,每个个体在不与其他个体发生作用的情况下是李雅普诺夫稳定的,与其他个体交流的信息是传感器测得的带有偏差的位置信息.当每个个体采取分布式线性控制协议时,整个群体的动力学行为,不仅和个体的动力学方程有关,而且和网络结构的代数特征有关.本文具体给出了群体出现全局渐近聚集、周期振荡和发散3种不同行为的代数判据.最后,仿真例子验证了本文结果的有效性.     

基于有向网络的多智能体系统快速一致性

针对具有二次积分动态的多智能体系统在有向网络下的快速一致性问题,提出了基于智能体当前状态和过去状态的快速一致性协议.利用矩阵理论和频域分析法,分别给出了多智能体系统达到静态一致性和动态一致性的充要条件,同时得到该协议能够使系统分别快速地达到静态一致和动态一致的过去状态区间.仿真示例验证了所提出协议的有效性.     

基于非光滑采样控制算法的二阶有向多智能体系统的一致性

针对二阶有向多智能体系统的一致性问题,在连续时间域和离散时间域分别提出一种非光滑控制协议.首先,提出一种连续时间非光滑一致性协议,通过李雅普诺夫理论和齐次系统理论,证明在无扰动情况下可以实现智能体状态的有限时间一致,而在有扰动情况下智能体状态之间的误差将收敛到一个与控制参数和外部扰动相关的范围内;然后,基于采样控制,提出离散非光滑一致性协议,进一步分析采样周期对智能体状态之间误差的影响,并给出误差收敛区间与控制参数、外部扰动和采样周期关系的显性表达式;最后,通过仿真实例验证理论的正确性和有效性.     

改进的有向传感器网络多中心部署算法*

针对单个节点非均匀有向传感器网络部署的局限,提出了多中心的节点部署算法PFMCA(Potential Field based Multi-Center Algorithm)。在部署中心概念及移动策略的基础上,能够保证多个监测中心的覆盖质量,同时实现对其余区域的均衡且尽可能高效的覆盖。仿真实验表明,本文提出的算法实现了对多个重点监测区域的高覆盖质量,且在多中心点间的区域具有更好的覆盖均衡性。     

Leader-following scaled consensus of second-order multi-agent systems under directed topologies

ABSTRACT

This paper investigates the leader-following scaled consensus problem of second-order multi-agent systems under directed topologies. Three novel leader-following scaled consensus protocols are designed. First, a novel scaled consensus protocol is proposed. It can guarantee the velocity of each agent in one sub-group exactly follow that of a leader, and the follower agents achieve scaled consensus. Second, another proposed protocol enables the agents' positions and velocities of one sub-group accurately track those of a leader, and the follower agents achieve scaled consensus. Third, consider the case where the leader's states available to one or multiple followers and the leader travels with a varying velocity, a novel scaled consensus tracking protocol is proposed. Sufficient and necessary conditions are obtained to guarantee scaled consensus tracking for the three cases,respectively. Finally, simulation examples are made to verify the effectiveness of the theoretical results.     

Robust consensus tracking of a class of second-order multi-agent dynamic systems

In this paper, we study the problem of robust consensus tracking for a class of second-order multi-agent dynamic systems with disturbances and unmodeled agent dynamics. Contrary to previous approaches, we design continuous distributed consensus protocols to enable global asymptotic consensus tracking. Our focus is on consensus protocol design and stability analysis which also leads to the derivation of sufficient conditions for consensus tracking. We first consider the case of undirected information exchange with a symmetric and positive definite information-exchange matrix. We develop an identifier for each agent to estimate the unknown disturbances and unmodeled agent dynamics. Based on the identifier, we develop a consensus tracking protocol to enable global asymptotic consensus tracking using local information obtained from neighboring agents. The closed-loop stability is proven using Lyapunov analysis theory and an invariance-like theorem. We then extend the approach to the case of directed information exchange, whose information-exchange matrix is only of full rank so that the approach for undirected graphs cannot be directly applied. We show that global asymptotic consensus tracking can still be enabled under the new derived sufficient conditions by designing a new identifier, which utilizes the estimated information exchanged from neighboring agents, and constructing a new Lyapunov function. Examples and numerical simulations are provided to validate the effectiveness of the proposed robust consensus tracking method.     

Decentralised regulation of nonlinear multi-agent systems with directed network topologies

This paper aims to address the leader–follower regulation problem of multi-agent systems with directed network topologies, where the agents are described by feedforward nonlinearities with the growth rate being unknown a priori. Both the state feedback regulation protocol and the output feedback regulation protocol are delicately constructed such that all the states of followers can converge to the leader state globally. In this paper, a model transformation is firstly performed and the leader–follower regulation problem can be transformed into a general regulation problem. Then, by introducing an appropriate state transformation, the regulation problem can be changed into a parameter determined problem. It is proved that the parameter can be determined by both the properties of M-matrices and the estimates of nonlinear terms. Finally, a numerical example is presented to show the feasibility of designed protocols.     

Impulsive positive observers and dynamic output feedback stabilization of positive linear continuous systems

This paper is concerned with the design and the synthesis of the impulsive positive observer (IPO) for positive linear continuous systems. The IPO can estimate the states for positive systems even when the measured output is only available at discrete‐time instants. In this paper, a time‐varying weighted copositive Lyapunov function is constructed, and the upper and lower bounds of impulsive intervals method combined with the convex combination technique are used to establish sufficient conditions for the existence of the IPO. Furthermore, the design of the dynamic output feedback controller based on the IPO is addressed to positively stabilize positive linear systems. Algorithms are given to design the IPO and the controller, respectively. Finally, two numerical examples are provided to show the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Realisation of linear time-varying systems

In this paper, the realisation problem of linear multi-input multi-output, time-varying systems is studied. The approach, based on the theory of non-commutative polynomial rings, yields explicit and simple formulas for computation of the state coordinates as well as for state equations in observable canonical form. The formulas are based on (left) Euclidean polynomial division.     

一类二阶非完整系统的镇定

研究一类二阶非完整系统的镇定问题. 通过状态和输入反馈变换将系统模型转换为二阶链式标准型, 并对标准型给出一种时变光滑指数镇定控制律. 所得结果应用于欠驱动平面刚体的镇定.     

On dynamic reconstruction of input in the second-order linear systems

Consideration was given to the problem of dynamic reconstruction of input in the second-order linear systems. Procedures for its real-time solution were specified. They feature dynamicity, which means that the current values of the approximated input are generated in real time, and stability, which means that for a sufficiently small measurement error approximation is arbitrarily precise.     

Consensus of multi-agent linear dynamic systems via impulsive control protocols

In this article, we introduce impulsive control protocols for multi-agent linear dynamic systems. First, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the consensus of the multi-agent linear dynamic systems by the theory of impulsive systems. Furthermore, how to select the discrete instants and impulsive matrices is discussed. The case that the topologies of networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.