Preassigned/fixed-time stochastic synchronization of complex networks via simpler nonchattering quantified adaptive control strategies

This paper investigates the preassigned-time (PAT) and fixed-time (FXT) synchronization of complex networks with stochastic disturbances, in which simpler nonchattering quantified adaptive controllers are designed. First, more relaxed conditions are proposed, and the settling time is calculated more precisely compared with existing results by utilizing some constructing comparison systems. Furthermore, different from existing results, the novel quantified adaptive controllers without sign function and linear feedback term not only are simpler but also can avoid chattering phenomenon. In addition, communication constraints and limited bandwidths are fully taken into account. Therefore, each parameter that needs to be transmitted will be quantified. Moreover, based on more relaxed conditions, several novel PAT control schemes are considered, in which the settling time can be preassigned based on actual demand. Finally, numerical simulation illustrates the effectiveness of the theories about the PAT and FXT synchronization.