This article addresses the problem of consensus in networks divided into subnetworks (also called clusters), where each node of the network graph represents an agent with linear dynamics. Each subnetwork is represented by a directed graph. Moreover, the agents in each cluster cannot communicate with agents from other clusters, except one single agent of each subnetwork, which is called a leader. These leaders interact some instant times via a fixed and strongly connected directed graph. An impulsive observer-based control protocol is proposed. Based on this proposed protocol, the collective network dynamics of multi-agent systems is described in the term of hybrid systems. The characterization of the global consensus value of this kind of networks is analyzed. Secondly, we show that the problem of consensus design for clustered networks can be indirectly solved by considering the stability of an equivalent system. Then, a sufficient condition for the asymptotical stability of this equivalent system is proposed. Finally, an algorithm properly selects the interaction network of the leaders, feedback gain, observer gain matrices, and coupling weights. This allows agents in the clustered network to enclose a prior fixed target. Simulation results are given to demonstrate the effectiveness of the theoretical results.

中文翻译：

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线性多智能体系统集群网络中基于脉冲观察者的控制

本文解决了划分为子网（也称为集群）的网络中的共识问题，其中网络图的每个节点代表一个具有线性动态的代理。每个子网都由一个有向图表示。此外，每个集群中的代理不能与来自其他集群的代理通信，除了每个子网的一个代理，称为领导者。这些领导者通过固定且强连接的有向图在某些瞬间进行交互。提出了一种基于脉冲观测器的控制协议。基于这个提议的协议，多代理系统的集体网络动态在混合系统的术语中被描述。分析了这种网络的全局共识值的表征。第二，我们表明，通过考虑等效系统的稳定性，可以间接解决集群网络的共识设计问题。然后，提出了该等效系统渐近稳定的充分条件。最后，算法正确选择领导者的交互网络、反馈增益、观察者增益矩阵和耦合权重。这允许集群网络中的代理包围一个预先固定的目标。仿真结果证明了理论结果的有效性。这允许集群网络中的代理包围一个预先固定的目标。仿真结果证明了理论结果的有效性。这允许集群网络中的代理包围一个预先固定的目标。仿真结果证明了理论结果的有效性。