Adaptive nonsingular terminal sliding mode control for synchronization of identical Φ6 oscillators

The main goal of this paper is to propose the adaptive nonsingular terminal sliding mode controllers for complete synchronization (CS) and anti-synchronization (AS) between two identical I broken vertical bar (6) Van der Pol or Duffing oscillators with presentations of system uncertainties and external disturbances. Unlike directly eliminating the nonlinear items of synchronized error system for sliding mode control schemes in the literature, the proposed adaptive controllers can tackle the nonlinear dynamics without active cancellation. The controllers can be implemented without known bounds of system uncertainties and external disturbances. Meanwhile, the feedback gains are not determined in advance but updated by the adaptive rules. Sufficient conditions are given based on the Lyapunov stability theorem and numerical simulations are performed to verify the effectiveness of presented schemes. The results show that the chaotic synchronization can be achieved accurately by the chattering free control.