Technical Correspondence Decentralized Adaptive Pinning Control for Cluster Synchronization of Complex Dynamical Networks

Abstract—In this brief, we investigate pinning control for cluster syn-chronization of undirected complex dynamical networks using a decen-tralized adaptive strategy. Unlike most existing pinning-control algorithms with or without an adaptive strategy, which require global information of the underlying network such as the eigenvalues of the coupling matrix of the whole network or a centralized adaptive control scheme, we propose a novel decentralized adaptive pinning-control scheme for cluster synchro-nization of undirected networks using a local adaptive strategy on both coupling strengths and feedback gains. By introducing this local adaptive strategy on each node, we show that the network can synchronize using weak coupling strengths and small feedback gains. Finally, we present some simulations to verify and illustrate the theoretical results. Index Terms—Cluster synchronization, complex dynamical network, local decentralized adaptive strategy, pinning control. I