Predictor-based super-twisting sliding mode observer for synchronisation of nonlinear chaotic systems with delayed measurements

The most used configuration for chaos synchronisation is the drive-response or master–slave pattern, where the response of chaotic systems at the receiver side must track the drive chaotic trajectory at the emitter side. The synchronisation is achieved by sending, through the public channel, a suitable control signal delivered by the emitter on its output to the receiver. One of the major problems encountered in this configuration is transmission delay which can degrade the synchronisation. In this paper, we focus on the synchronisation problem of nonlinear chaotic systems in the presence of output transmission delay. In the new proposed method, the slave system is made up of a super-twisting sliding mode observer and a predictor arranged in cascade in order to compensate for the delayed transmission signal from the transmitter to the receiver. The observer estimates the delayed states and the predictor provides the estimated states at the current time. The convergence conditions of the proposed method are established. Numerical examples are given. The computer simulation results are provided to demonstrate the effectiveness of the proposed synchronisation approach.