Chaotic synchronization and convergence of second-order time-varying parameter systems using a hybrid barrier Lyapunov function-based controller with embedded indirect neural approximation for noise suppression

A novel hybrid Barrier Lyapunov Function (BLF) is introduced in both virtual and actual control law development, to suppress synchronization errors and attain robust convergence for highly complex systems. Specifically, we originally propose a fixed-time neural adaptive controller for the synchronization of second-order chaotic systems. The controller set-up is recursively updated based on a fixed-time back-stepping technique, whilst a neural network is further embedded to suppress stochasticity and inherent uncertainties induced by unknown disturbances. As opposed to a conventional neural approximation, an “indirect” approach is adopted for parsimonious optimization and fast convergence. Consequently, only one learning parameter is updated under a nowcasting-fashion design, resulting to a significant minimization of computational burden. We prove the robustness of the system's fixed-time stability and validate its enhanced synchronization properties through an elaborate Lyapunov analysis and an extensive simulation investigation, in the presence of induced stochasticity by various external disturbances. Simulation results indicate that our approach can acquire the more excellent synchronization performance than the existing controller.