Synchronizing different chaotic systems using active sliding mode control. (English) Zbl 1142.93394

Summary: An active sliding mode controller is designed to synchronize three pairs of different chaotic systems (Lorenz-Chen, Chen-Lü, and Lü-Lorenz) in drive-response structure. It is assumed that the system parameters are known. The closed loop error dynamics depend on the linear part of the response systems and parameters of the controller. Therefore, the synchronization rate can be adjusted through these parameters. Analysis of the stability for the proposed method is derived based on the Lyapunov stability theorem. Finally, numerical results are presented to show the effectiveness of the proposed control technique.


93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93B12 Variable structure systems
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