Quantized adaptive pinning control for fixed/preassigned-time cluster synchronization of multi-weighted complex networks with stochastic disturbances

The article studies preassigned-time (PAT) and fixed-time (FXT) cluster synchronization of multi-weighted complex networks (CNs) with stochastic disturbances through designing quantized adaptive pinning control scheme. Firstly, the controller can achieve lower control costs and save communication channels. By designing a novel and appropriate Lyapunov function, combining the characteristics of Wiener process and utilizing a method of comparison system, FXT synchronization criteria of CNs are proposed. The FXT criteria can be more widely applied in directed and undirected multi-weighted CNs. Besides, the PAT cluster synchronization is also investigated by utilizing a novel control scheme that the gains of controller are finite, where the synchronization time can be preassigned based on realistic situation. The effectiveness of theoretical results is illustrated via simulations.