On predefined-time synchronisation of chaotic systems

Abstract 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 Rossler systems, is presented to show the applicability of the proposed scheme in a different chaotic system.

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