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

Abstract

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.

Keywords:

• Nonlinear system
• sliding modes observer
• super-twisting algorithm
• chaotic synchronisation
• predictor

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Ahcene Hamoudi

A. Hamoudi received his master degree in automatic from the Mouloud Mammeri University, Tizi-Ouzou, Algeria, in 2016. His is currently working towards a Ph.D. degree in automatic at the University Mouloud Mammeri, Tizi-Ouzou, Algeria. His research interests include synchronisation of chaotic systems, delay systems, nonlinear systems and nonlinear observers.

Nadia Djeghali

N. Djeghali received the Ph.D. degree from the Mouloud Mammeri University, Tizi Ouzou, Algeria, in 2013. She is currently an Associate Professor at the University of Mouloud Mammeri. She carries out research at the Laboratoire de Conception et Conduite des Systèmes de Production (L2CSP), Mouloud Mammeri University. Her research interests include diagnostic, fault tolerant control, nonlinear systems, delay systems, nonlinear observers, sliding mode control and fractional-order systems.

Maamar Bettayeb

M. Bettayeb received the Ph.D. degree in Electrical Engineering from University of Southern California, Los Angeles, in 1981. He has been Professor at University of Sharjah UAE since August 2000. He is also Distinguished Adjunct Professor at the College of Engineering, King Abdulaziz University, Jeddah, KSA. His research interests are in H∞ optimal control, model reduction, signal and image processing, networked control systems, fractional dynamic modelling and control, soft computing, wavelets, renewable energies and engineering education.