符号网络下一类非线性二分一致性系统的跟踪控制

研究具有对抗交互的一类非线性多智能体系统的二分一致性跟踪控制问题,借助有向符号图刻画智能体之间的通信关系,并假定符号图是结构平衡的.进一步,借助符号图网络对二分一致性跟踪问题进行公式化描述.基于最近邻原则,结合拉普拉斯矩阵、牵制矩阵、符号函数、耦合增益参数等,设计分布式控制律.利用Barbalat引理和李亚谱诺夫函数证明整个闭环系统的渐近稳定性,在保持闭环系统稳定的条件下推导出耦合增益的下界.最后通过仿真验证所提出方法的有效性.     

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.     

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。     

多智能体网络系统的能控性代数条件

能控性是多智能体系统研究的核心问题,主要包括结构可控性和精准可控性。对多智能体系统的模型和能控性代数条件进行了总结。在相对协议和绝对协议条件下,运用图论和矩阵论的知识系统分析了多智能体系统能控性的代数条件。按照同质多智能体到异质多智能体的顺序,对现有的多智能体系统模型和代数条件进行了梳理,并在已有结论的基础上对多智能体系统能控性的代数条件进行了改善,进一步提出了新的代数条件。多智能体能控性代数条件的改进大大简化了能控性的计算量。     

带强连通分支的多智能体系统可控包含控制

研究有强连通子图拓扑结构的有向多智能体系统领导者选择及可控包含控制问题.根据网络拓扑结构,智能体被分为两类:单元智能体和一般智能体.首先设计强连通子图中个体组成的单元智能体的一致性协议实现各个单元的一致;后由单元智能体和一般智能体构成新的拓扑结构,结合复杂网络可控性理论与二分图最大匹配算法确定满足网络可控的最少领导者集合,并为所有智能个体设计相应的控制协议,驱使跟随者渐近收敛到多个领导者组成的动态凸包中,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.     

通信受限的多智能体系统二分实用一致性

针对存在量化数据、通信时滞等通信约束以及带有竞争关系的多智能体系统, 研究其二分实用一致性问题, 提出了一种基于量化器的分布式控制协议. 该协议基于结构平衡拓扑假设, 通过规范变换将具有竞争关系系统转变为具有非负连接权重系统, 使二分实用一致性问题转变为一般实用一致性问题. 利用微分包含理论、菲利波夫解的框架、代数图论以及Lyapunov稳定性理论, 证明了在本文所提控制策略下, 具有竞争关系的多智能体系统能实现二分实用一致, 即智能体状态收敛至模相同但符号不同的可控区间, 并给出了误差收敛上界值. 仿真试验进一步验证了理论结果的有效性.     

基于双索引的近似子图匹配

越来越多的大型复杂网络使得图结构的研究变得日益重要,其中近似子图查询备受关注。为了提高查询效率,利用顶点的邻接关系特征为每个顶点建立索引,减少了匹配顶点的数量;并基于结构和标签对大型数据图进行划分,缩小了匹配时的搜索空间。利用离线时建立的双索引,查询时首先利用顶点间的近邻关系判定公式过滤掉大量不满足匹配关系的候选顶点,然后在一定的划分空间中进行边的匹配。真实数据集中的实验表明,与单纯的划分方法或近邻关系索引相比较,双索引机制对于查询的效率和准确率方面均有明显改善。     

复杂无向网络连通性的一种高效判定算法

通信网络的拓扑结构连通性是多智能体系统一致性控制或编队控制等的理论前提.以往, 各种多智能体系统一致性控制或编队控制方面的文献仅侧重于控制协议、智能体动力学模型和控制律设计, 而缺乏对多智能体通信网络拓扑结构的连通性研究.网络连通性高效判定算法不仅是大规模多智能体系统一致性控制或编队控制的保证, 而且在图论、现代移动通信、计算机与交通等各种网络中有着重要和广泛的应用.针对复杂无向网络的连通性问题, 本文给出了一种新的高效判定算法、以及该算法的时间复杂度和空间复杂度的上界.该算法具有非常低的时间复杂度和空间复杂度, 且便于计算机实现, 因而具有重要的理论意义和广泛的实用价值.     

网络环境下固定拓扑的多电机领航跟随控制

基于多智能体一致性理论,从领航跟随控制的角度解决网络环境下多电机的同步控制问题,其中考虑了网络时延对同步控制的影响。每个电机均被视为一个智能体,且每个智能体能且只能得到其邻域的输出测量信息,在此条件下,研究了在有向固定网络拓扑情况下多电机系统的同步控制问题。为了解决网络时延对电机同步控制的影响,提出了一种带有分布式观测器的时延一致性控制协议,应用 Lyapunov稳定性理论证明了若单个电机是能观能控的,只要网络连接满足简单的拓扑结构,则多电机系统能够达到领航跟随一致性。最后通过仿真实验验证了该方法的正确性和有效性。     

带有多个时变时滞的一阶多智能体系统的H∞包围控制

研究带有多个时变时滞的一阶多智能体系统在有向网络拓扑下的_∞包 围控制问题.首先,通过引入收敛性向量函数,将所讨论问题转化为一般时滞系统的_∞控制问题.然后,通过构造适当的Lyapunov-Krasovskii泛函,利用Lyapunov稳定性理论得到多智能体系统实现包围控制的充分条件,同时求得时变通信时滞的最大容许值.另外,在有外部干扰的情况下,得到了多智能体系统具有_∞包围控制性能常数的充分条件.最后,通过数值仿真实验验证了所得结果的有效性.     

Bipartite tracking of homogeneous and heterogeneous linear multi-agent systems

In this paper, we consider bipartite tracking of linear multi-agent systems with a leader. Both homogeneous and heterogeneous systems are investigated. The communication between agents is modelled by a directed signed graph, where the negative (positive) edges represent the antagonistic (cooperative) interactions among agents. Linear Quadratic Regulator (LQR)-based approach is used to derive the distributed protocol for the follower agent to achieve bipartite tracking of the leader. It is shown that solving the bipartite tracking problem over the structurally balanced signed graph is equivalent to solving the cooperative tracking problem over a corresponding graph with nonnegative edge weights. This bridges the gap between the newly raised bipartite tracking problem and the well-studied cooperative tracking problem. Three novel control protocols are proposed for both cooperative and bipartite output tracking of heterogeneous linear multi-agent systems. Numerical examples are given to show the effectiveness of our control protocols.     

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.     

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.     

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.     

Controllability and observability of switched multi-agent systems

This paper considers controllability and observability of switched multi-agent systems, which are composed of continuous-time and discrete-time subsystems. First, a controllability criterion is established in terms of the system matrices. Then, by virtue of the concepts of the invariant subspace and the controllable state set, a method is proposed to construct the switching sequence to ensure controllability of switched multi-agent systems, and a necessary and sufficient condition is obtained for controllability. Moreover, a necessary controllability condition is derived in terms of eigenvectors of the Laplican matrix. With respect to observability, two necessary and sufficient algebraic conditions are obtained. Finally, simulation examples are provided to illustrate the theoretical results.     

对抗网络下时滞非线性多智能体系统固定时间二分一致性

本文针对一类存在输入时延的非线性多智能体系统,研究了其在结构平衡的无向符号图下的固定时间二分一致性问题.首先,本文针对智能体间相互合作与相互竞争的关系,设计了一类存在输入时延的多智能体系统固定时间分布式一致性控制协议,使得系统状态在固定时间内收敛到数值相同但符号相反的两个值,且收敛时间上界与初始状态无关.随后,利用Lyapunov稳定性理论和代数图论给出了在存在输入时延的情况下多智能体系统实现固定时间二分一致性的充分条件和收敛时间的上界值,证明了控制算法的稳定性.最后,仿真实例验证了所提固定时间二分一致性算法和理论结果的有效性.     

Controllability and observability of multi-agent systems with heterogeneous and switching topologies

ABSTRACT

This paper focuses on controllability and observability of multi-agent systems with heterogeneous and switching topologies, where the first- and the second-order information interaction topologies are different and switching. First, based on the controllable state set, a controllability criterion is obtained in terms of the controllability matrix corresponding to the switching sequence. Next, by virtue of the subspace sequence, two necessary and sufficient algebraic conditions are established for controllability in terms of the system matrices corresponding to all the possible topologies. Furthermore, controllability is considered from the graphic perspective. It is proved that the system is controllable if the union graph of all the possible topologies is controllable. With respect to observability, two sufficient and necessary conditions are derived by taking advantage of the system matrices and the corresponding invariant subspace, respectively. Finally, some simulation examples are worked out to illustrate the theoretical results.     

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.