Pinning synchronization control based on disturbance observer with an RBF neural network for multi-layer complex networks

The pinning synchronization control for multi-layer networks with external disturbance and unknown uncertainties is studied. For the unknown bounded uncertainty, an adaptive radial basis function neural network (RBFNN) is designed to approximate it. Based on the RBFNN, a disturbance observer is constructed for the exogenous disturbance. Then, a multi-layer network pinning synchronization controller is designed, and the controller is only applied to some of the nodes, which saves control resources and ensures the smooth implementation of control. Through the Lyapunov stability analysis, an adaptive law was designed, providing sufficient conditions to ensure the realization of pinning synchronization in multi-layer networks. Finally, the proposed strategy was simulated in a two-layer network, and the results demonstrated the effectiveness of the proposed strategy.