基于拓扑结构和个体动态层面的多智能体系统可控性分析

针对一般线性多智能体系统中网络拓扑及个体动态这两个层面的可控性对系统整体可控性的关系进行了研究，提出了一种新的描述一般线性多智能体系统的模型。利用PBH(Popov-Belevitch-Hautus)判据，得到并证明了在此模型下多智能体系统可控性在网络拓扑结构与个体动态层面的充要条件。结合具体的例子解释了系统矩阵中出现重复特征值时对定理2充分性的影响，并且提供了一种避免重复特征值出现的方法。特别地，推导出了此模型下系统矩阵为实对称矩阵这一特殊情况时可以判定该系统不可控的两种判定条件，即比较系统矩阵中最大的特征值代数重数与控制矩阵中1元素的个数，满足条件即判定系统不可控。     

二阶邻居协议下多智能体系统能控能观性保持

为了研究多智能体系统的一致性特点及能控、能观性保持策略,分析了具有时变拓扑结构的多智能体系统在一阶邻居协议和二阶邻居协议下的一致性速度,针对拓扑结构的特殊性,利用结构能控性性质和拉普拉斯矩阵第二小特征值与一致性速度之间存在的关系设计出一种使能控性和能观测性保持的控制策略。此外,得出多智能体系统在二阶邻居协议下,具有更快的一致性速度的结论。文中2个主要定理分别通过算例和仿真进行验证,算例和仿真结果与定理结论一致。     

多智能体系统能控性研究进展

能控性问题是多智能体协调控制领域中一个基本又十分重要的研究课题.本文对多智能体系统能控性问题的研究现状进行综述.介绍了多智能体能控性领域的基本问题和特点,并结合智能体自身动力学与邻居交互协议,从拓扑结构角度对该领域当前的研究热点和前沿进行分析阐述.进一步,对结构能控性的研究成果进行归纳总结,并对能观测性、可镇定性和复杂网络能控性等相关问题进行阐述.最后给出了仍需解决的问题和可能的研究方向.     

切换网络下时变线性多智能体系统的指数同步

研究切换网络下时变连续线性多智能体系统的同步问题. 在智能体动态满足一致完全可控性条件下, 设计出同步协议. 通过将多智能体系统同步问题表示为矩阵无穷乘积形式并论证矩阵无穷乘积指数收敛到0, 给出了多智能体系统指数同步结论. 最后以仿真实例验证本文结论.     

异构多无人机网络化协同控制系统的可控性

研究具有Leader-Follower结构和分布式通信拓扑的异构多无人机网络化分布式协同控制系统的可控性问题. 基于同构网络的受控一致性思想建立了异构多飞行器网络控制系统的动态模型; 并针对该动态模型的不同形式, 基于代数图论和传统的控制理论, 分别得到了异构多无人机网络化协同控制系统的可控性条件, 尤其是可控性与该网络化系统中通信拓扑之间的关系; 然后分析且提出了改善系统可控性的可行性方法. 最后仿真结果验证了本文相关结论的正确性.     

无速度输入多智能体系统的一致性

本文研究了有无引导者的多智能体系统在非线性协议下的一致性问题.当智能体速度信息无法获知时,分别针对有无引导者的多智能体系统设计了包含辅助系统和智能体相对位移信息的非线性分布式协议.借助图论、Lyapunov稳定性理论、Barbalat引理等方法,推导出有无引导者的多智能体系统在连通无向通讯网络中实现一致的充分条件,其次,设计了一种新的能使引导–追随者多智能体系统在有向通讯网络中实现期望一致的协议.最后,数值仿真验证了结果的正确性.     

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。     

有向符号网络的边能控性研究

符号网络是一类具有正负符号特征的网络.在多智能体系统中,符号网络能够描述智能体之间的合作与对抗交互关系,因此受到学者的广泛关注.本文主要研究有向符号网络的边能控性.首先,对具有符号网络的多智能体系统边动力学进行建模,得到边能控性模型.其次,从网络拓扑结构角度对边能控子空间进行定量刻画,利用有向符号网络的距离和等价划分得到能控子空间的上下界估计.进一步,讨论了符号网络边能控性与顶点能控性的关系.所得结果表明:当顶点符号图为结构非平衡时,符号网络的边能控性与顶点能控性等价.最后,通过仿真结果验证所得理论的有效性.     

自旋量子系统的可控李代数计算

动态系统可控性同是经典和量子控制中研究的一个基本问题,本文研究了单自旋和双自旋量子系统的可控李代数的计算.首先基于量子系统可控的等价性条件,通过单量子系统Hamiltonian算符的李括号运算,给出了与基系数相关的系统可控的充要条件.然后利用Cartan分解方法构造了李代数su(4)的矩阵基,同时根据可控性基本定理提出了Hamiltonian算符多重李括号的计算方法及系统的可控性判据.     

动态非线性智能体网络的渐近一致协议

提出了由一般非线性方程描述的多个智能体组成的网络达成渐近一致的概念,以及多动态智能体网络的渐近一致协议问题,介绍了表征网络信息流的图论知识,讨论了在一定的网络信息流拓扑结构情况下,使用非线性控制理论得出的多动态智能体网络最终达成渐近一致的协议的形式、计算方法及其存在条件。运用该一致协议对多无人机系统进行编队控制,其仿真结果表明了该一致协议的应用领域和有效性。     

Controllability of multi-agent systems with time-delay in state and switching topology

In this article, the controllability issue is addressed for an interconnected system of multiple agents. The network associated with the system is of the leader–follower structure with some agents taking leader role and others being followers interconnected via the neighbour-based rule. Sufficient conditions are derived for the controllability of multi-agent systems with time-delay in state, as well as a graph-based uncontrollability topology structure is revealed. Both single and double integrator dynamics are considered. For switching topology, two algebraic necessary and sufficient conditions are derived for the controllability of multi-agent systems. Several examples are also presented to illustrate how to control the system to shape into the desired configurations.     

Controllability of discrete-time multi-agent systems with directed topology and input delay

This paper investigates the controllability of first-order and second-order discrete-time multi-agent systems with directed topology and input delay. The problem is studied in the leader–follower framework where a number of agents are selected to be leaders and serve as control inputs to all other agents. Sufficient and necessary conditions are derived for the controllability of first-order discrete-time multi-agent systems. With sampling period and feedback gain satisfying certain conditions, it is proved under three different protocols that the controllability of second-order discrete-time multi-agent systems is equivalent to that of a pair of submatrices of Laplacian matrix. In addition, the controllability of both first-order and second-order discrete-time multi-agent systems with input delay is shown, through some transformations, to be equivalent to that of the transformed non-delayed systems. Finally, some simulation examples are given to illustrate the theoretical results.     

Graph-theoretic characterisations of structural controllability for multi-agent system with switching topology

This article considers the controllability problem for multi-agent systems. In particular, the structural controllability of multi-agent systems under switching topologies is investigated. The structural controllability of multi-agent systems is a generalisation of the traditional controllability concept for dynamical systems, and purely based on the communication topologies among agents. The main contributions of this article are graph-theoretic characterisations of the structural controllability for multi-agent systems. It turns out that the multi-agent system with switching topology is structurally controllable if and only if the union graph 𝒢 of the underlying communication topologies is connected (single leader) or leader–follower connected (multi-leader). Finally, this article concludes with several illustrative examples and discussions of the results and future work.     

Controllability improvement for multi-agent systems: leader selection and weight adjustment

For an uncontrollable system, adding leaders and adjusting edge weights are two methods to improve controllability. In this paper, the controllability of multi-agent systems under directed topologies is studied, especially on the leader selection problem and the weight adjustment problem. For a multi-agent system, necessary and sufficient algebraic conditions for controllability with fewest leaders are proposed. To improve controllability by adjusting edge weights, the system is supposed to be structurally controllable, which holds if and only if the communication topology contains a spanning tree. It is also proved that the number of the fewest edges needed to be assigned on new weights equals the rank deficiency of controllability matrix. In addition, a leader selection algorithm and a weight adjustment algorithm are presented. Simulation examples are provided to illustrate the theoretical results.     

多智能体系统在分布式采样控制下的动力学行为

本文运用图论、矩阵分析和现代控制理论等工具, 研究信息网络传输下多智能体系统的协调控制和动力学行为. 假设每个智能体通过数字化网络传感器获得其邻近智能体的位置状态,而且多智能体系统采取分布式线性控制协议. 每个智能体被描述为一个简单的采样系统,多智能体系统转化为混合动力学系统. 研究结果表明,多智能体系统所呈现的渐近聚集、周期振荡和发散动力学行为不仅和网络结构的代数特征有关, 而且和每个智能体的动力学方程、采样周期有关. 本文给出了具体精确的代数判据. 仿真例子进一步验证了本文结果的有效性.     

多智能体系统可控性的图论刻画

研究领航者-跟随者结构多智能体系统的可控性问题.利用松弛的等价分化刻画了系统可控性与信息拓扑结构之间的关系,为系统可控性提供了基于图论的判别方法.基于置换群理论将对称的概念推广到多领航者系统,并证明了3种图论工具（对称性、等价分化和松弛的等价分化）之间的包含关系.仿真结果验证了所提出方法的有效性.     

Controllability analysis of multi-agent systems with directed and weighted interconnection

In this article, we investigate the controllability of multi-agent systems with leaders as control inputs, where the interconnection is directed and weighted. We employ weight-balanced partition to classify the interconnection graphs, and study the controllable subspaces with given nontrivial weight-balanced partition. We also provide two necessary and sufficient graph conditions on structural controllability and strong structural controllability. Moreover, we consider the effect of the zero row-sum restrictions of the system matrices on structural controllability.     

Controllability of heterogeneous multi-agent systems under directed and weighted topology

This paper considers the controllability problem for both continuous- and discrete-time linear heterogeneous multi-agent systems with directed and weighted communication topology. First, two kinds of neighbour-based control protocols based on the distributed protocol of first-order and second-order multi-agent systems are proposed, under which it is shown that a heterogeneous multi-agent system is controllable if the underlying communication topology is controllable. Then, under special leader selection, the result shows that the controllability of a heterogeneous multi-agent system is solely decided by its communication topology graph. Furthermore, some necessary and/or sufficient conditions are derived for controllability of communication topology from algebraic and graphical perspectives. Finally, simulation examples are presented to demonstrate the effectiveness of the theoretical results.