Observer-Based Intra-Cluster Lag Consensus of Multi-Agent Systems via Intermittent Adaptive Pinning Control

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.