Fixed-time stochastic outer synchronization in double-layered multi-weighted coupling networks with adaptive chattering-free control

Abstract

The problem for fixed-time outer synchronization of double-layered multi-weighted coupled complex networks with stochastic effects is considered in this paper. To suppress chattering in synchronization, an adaptive chattering-free control algorithm is designed. Based upon the Lyapunov stability theory, some sufficient criteria for the adaptive stochastic outer synchronization are proposed. The designed adaptive chattering-free controller and the sufficient conditions can be applicable to not only the fixed-time stochastic synchronization of double-layered multi-weighed undirected networks, but also the fixed-time stochastic synchronization of double-layered multi-weighted directed networks. Our theoretical results indicate that the settling time is related to the size of dynamic networks, the dimension of each node and the designed adaptive controllers in the fixed-time stochastic outer synchronization. The effectiveness of our derived theoretical framework is illustrated via simulation examples.