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

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.