Synchronization of uncertain chaotic systems based on optimal and variable structure control

This paper presents synchronization of two identical uncertain chaotic systems using combination of optimal theory and variable structure control. An adaptable variable structure control for compensating nonlinear parts and uncertainties of chaotic systems, and a quadratic optimal regulation for synchronizing linear part of chaotic systems are designed. Asymptotic stability of error dynamical system is proved using Lyapunov direct method. To show the effectiveness of the proposed controller, chaotic Lu system is considered as the case study. Simulation results are very promising.