On predefined-time synchronisation of chaotic systems

• Published in: Chaos, solitons and fractals Vol. 122; pp. 172 - 178
• Main Authors: Anguiano-Gijón, Carlos Alberto, Muñoz-Vázquez, Aldo Jonathan, Sánchez-Torres, Juan Diego, Romero-Galván, Gerardo, Martínez-Reyes, Fernando
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-05-2019
• Subjects: Chaos; Control Lyapunov-function; Predefined-time stability; Secure communication; Sliding mode control; Chaos; Predefined-time stability; Secure communication; Control Lyapunov-function; Sliding mode control
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2019.03.015

•An active control algorithm for predefined-time synchronisation of chaotic systems.•An application to fast and secure communication systems.•A numerical study based on simulations, comparing the proposed method to several different schemes.•A novel characterisation for predefined-time stability.•The predefined-time synchronisation is demonstrated based on the Lyapunov framework.
An active control Lyapunov-function design for predefined-time synchronisation of chaotic systems, based on the Lorenz attractor, is proposed in this paper. The proposed controller guarantees that before a known time, which is predefined during the control design, two chaotic systems are synchronised, enforcing a predefined-time sliding mode synchronisation. Numerical simulations are presented in order to show the reliability of the proposed method. Firstly, an application to secure communication is addressed, showing that, after the synchronisation is achieved, the exact message reconstruction is performed through a two-channel communication protocol, one channel for transmitting the message, and the other one for maintaining the synchronisation. An additional simulation case, about the synchronisation of two Rössler systems, is presented to show the applicability of the proposed scheme in a different chaotic system.