A generalized finite-time analytical approach for the synchronization of chaotic and hyperchaotic systems

Abstract

Purpose

The purpose of this paper is to develop some interesting results in the field of chaotic synchronization with a new finite-time controller to reduce the time of convergence.

Design/methodology/approach

This article proposes a finite-time controller for the synchronization of hyper(chaotic) systems in a given time. The chaotic systems are perturbed by the model uncertainties and external disturbances. The designed controller achieves finite-time synchronization convergence to the steady-state error without oscillation and elimination of the nonlinear terms from the closed-loop system. The finite-time synchronization convergence reduces the hacking duration and recovers the embedded message in chaotic signals within a given preassigned limited time. The free oscillation convergence keeps the energy consumption low and alleviates failure chances of the actuator. The proposed finite-time controller is a combination of linear and nonlinear parts. The linear part keeps the stability of the closed-loop, the nonlinear part increases the rate of convergence to the origin. A generalized form of analytical stability proof is derived for the synchronization of chaotic and hyper-chaotic systems. The simulation results provide the validation of the accomplish synchronization for the Lu chaotic and hyper-chaotic systems.

Findings

The designed controller not only reduces the time of convergence without oscillation of the trajectories which can run the system for a given time domain.

Originality/value

This work is originally written by the author.

Citation

Haris, M., Shafiq, M., Ibrahim, A. and Misiran, M. (2021), "A generalized finite-time analytical approach for the synchronization of chaotic and hyperchaotic systems", Multidiscipline Modeling in Materials and Structures, Vol. 17 No. 3, pp. 681-697. https://doi.org/10.1108/MMMS-06-2020-0131