Synchronization and adaptive anti-synchronization control for Lorenz systems under channel noise with applications

This paper studies synchronization and adaptive anti-synchronization control for Lorenz systems with applications to secure communication, where the transmission channel is subject to noise disturbance and the parameters of the Lorenz systems are allowed to be uncertain. Based on the methods of the Lyapunov function, input-to-state stability theory, nonlinear parametric variation, and the Barbalat Lemma, estimates for errors of synchronization and adaptive anti-synchronization are derived. These estimates help to design the feedback control and adaptive control laws with relatively small synchronization error bounds. Moreover, the information signal error in secure communication is also derived, which is used to design a secure communication scheme with a lower disturbance from channel noise and with higher security. Simulations are given to demonstrate the results.