The intra-cluster lag consensus means that the agents in the same cluster can achieve lag consensus asymptotically while the agents in different clusters can achieve different consensus. In this paper, the authors investigate the observer-based intra-cluster lag consensus problems of multi-agent systems (MASs) with general linear dynamics and nonlinear dynamics via intermittent adaptive pinning control. The interaction network is considered to be weakly connected, i.e., it is not necessary to be strongly connected, in-degree balanced or contain a directed spanning tree. To realise the intra-cluster lag consensus, a class of observers is designed to estimate the states of followers. Then a class of observer-based intermittent adaptive pinning control protocols is proposed according to the difference that the agents receive information source. Moreover, the pinning gains are designed to be intermittent adaptive and have an exponential convergence rate, which will effectively reduce communication costs, avoid the pinning gains being larger than those needed in real applications and guarantee the pinning gains quickly converge to steady value. Correspondingly, some sufficient consensus criteria are derived and rigorous proofs are given based on matrix theory and Lyapunov stability theory. Finally, the effectiveness for the proposed intermittent adaptive pinning control strategy is validated by a numerical simulation.

集群内滞后共识是指同一集群中的智能体可以渐近地达成滞后共识，而不同集群中的智能体可以达成不同的共识。在本文中，作者通过间歇性自适应钉扎控制研究了具有一般线性动力学和非线性动力学的多智能体系统（MAS）的基于观察者的集群内滞后一致问题。交互网络被认为是弱连接的，即不需要强连接、度内平衡或包含有向生成树。为了实现集群内滞后共识，设计了一类观察者来估计追随者的状态。然后根据Agent接收信息源的差异，提出一类基于观测器的间歇性自适应钉扎控制协议。此外，钉扎增益被设计为间歇自适应并具有指数收敛速度，这将有效降低通信成本，避免钉扎增益大于实际应用所需的值，并保证钉扎增益快速收敛到稳定值。相应地，基于矩阵理论和李亚普诺夫稳定性理论，推导了一些充分的共识准则并给出了严格的证明。最后，通过数值模拟验证了所提出的间歇性自适应钉扎控制策略的有效性。