Title: Anti-synchronisation of identical chaotic systems via novel sliding control and its application to a novel chaotic system

Authors: Sundarapandian Vaidyanathan; Sivaperumal Sampath

Addresses: Research and Development Centre, Vel Tech University, Avadi, Chennai-600 062, Tamil Nadu, India ' Department of Electronics and Communication Engineering, Vel Tech University, Avadi, Chennai-600 062, Tamil Nadu, India

Abstract: This research work investigates anti-synchronisation of identical chaotic systems via a novel sliding control method. Explicitly, a general result is derived for the anti-synchronisation of identical chaotic systems using the novel sliding control method. This paper also announces a novel 3D chaotic system with four quadratic nonlinearities. The Lyapunov exponents of the novel chaotic system are obtained as L₁ = 3.7828, L₂ = 0 and L₃ = −18.7651 while the Kaplan-Yorke dimension of the novel chaotic system is obtained as D_KY = 2.2016. The qualitative properties of the novel chaotic system are discussed in detail. As an application of the general control result, a sliding mode controller is derived for achieving anti-synchronisation of the identical novel chaotic systems for all initial conditions. Numerical simulations have been shown to depict the phase portraits of the novel chaotic system and the sliding mode controller design for the anti-synchronisation of identical novel chaotic systems.

Keywords: chaos theory; chaotic systems; chaos synchronisation; anti-synchronisation; sliding mode control; SMC; Lyapunov stability theory; numerical simulation; controller design.

DOI: 10.1504/IJMIC.2017.082484

International Journal of Modelling, Identification and Control, 2017 Vol.27 No.1, pp.3 - 13

Received: 08 Jun 2015
Accepted: 08 Jun 2015
Published online: 27 Feb 2017 *

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