Title: Synchronise a new class of noise-perturbed hyper-chaotic systems by adaptive sliding mode control

Authors: Ran Zhen; Jie Liu; Xueli Wu; Xiaojing Wu; Quanmin Zhu; Ying Wang; Hassan Nouri

Addresses: Department of Electrical Engineering, Hebei University of Science and Technology, 26 Yuxiang Street, Shijiazhuang, 050018, China; Engineering Design and Mathematics, University of the West of England, Frenchay Campus, Coldharbour, Lane Bristol, BS16 1QY, UK ' Department of Electrical Engineering, Hebei University of Science and Technology, 26 Yuxiang Street, Shijiazhuang, 050018, China ' Department of Electrical Engineering, Hebei University of Science and Technology, 26Yuxiang Street, Shijiazhuang, 050018, China; Institute of Electrical Engineering, Yanshan University, 438 Hebei West Street, Qinhuangdao, 06604, China ' Department of Electrical Engineering, Hebei University of Science and Technology, 26 Yuxiang Street, Shijiazhuang, 050018, China ' Engineering Design and Mathematics, University of the West of England, Frenchay Campus, Coldharbour, Lane Bristol, BS16 1QY, UK ' Department of Electrical Engineering, Hebei University of Science and Technology, 26 Yuxiang Street, Shijiazhuang, 050018, China ' Engineering Design and Mathematics, University of the West of England, Frenchay Campus, Coldharbour, Lane Bristol, BS16 1QY, UK

Abstract: This paper proposes an adaptive sliding mode control strategy for an introduced new hyper-chaotic system of Chen with the noise-perturbed. Based on the Lyapunov stability theory and variable structure control method, the adaptive sliding surface and adaptive controller are designed, to produce asymptotic convergence of the errors between the states of the master system and the states of the slave system. A single signal control is suggested based on adaptive sliding mode control to synchronise the noise-perturbed new hyper-chaotic systems with the same structure. Numerical simulations are presented to verify the effectiveness of the synchronisation scheme.

Keywords: synchronisation; hyper-chaotic systems; adaptive control; sliding mode control; SMC; parameter perturbation; Lyapunov stability theory; variable structure control; VSC; controller design; numerical simulation.

DOI: 10.1504/IJMIC.2013.056189

International Journal of Modelling, Identification and Control, 2013 Vol.20 No.2, pp.164 - 173

Published online: 27 Sep 2014 *

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