Cluster synchronization in community network with nonidentical nodes via intermittent pinning control

In this paper, cluster synchronization in community network with nonidentical nodes is investigated. By combining intermittency with a pinning control scheme, some effective controllers are designed. In the control scheme, only one node in each community is controlled and coupling weights of a spanning tree in each community are enhanced. Based on the Lyapunov function method and mathematical analysis technique, two results for achieving cluster synchronization are obtained. Noticeably, by introducing an adaptive strategy, some universal adaptive intermittent pinning controllers are designed for different networks. Finally, two numerical simulations are performed to verify the correctness of the derived results.

Synchronization of Complex Networks with Coupling Delays via Adaptive Pinning Intermittent Control

The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the methods of the adaptive control, pinning control and periodically intermittent control. Based on the piecewise Lyapunov stability theory, some less conservative criteria are derived for the global exponential synchronization of the complex dynamical networks with coupling delays. And several corresponding adaptive pinning feedback synchronization controllers are designed. These controllers have strong robustness against the coupling strength and topological structure of the network. Using the delayed nonlinear system as the nodes of the networks, a numerical example of the complex dynamical networks with nonlinear coupling delays is given to demonstrate the effectiveness of the control strategy.

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.