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Parameters identification and dual synchronization between different chaotic and hyperchaotic systems. (English) Zbl 1427.93102

Summary: This paper investigates the adaptive dual synchronization of completely different four chaotic and hyperchaotic systems with unknown parameters. Based on the Lyapunov stability theory, an efficient adaptive synchronization controller is constructed that converges the synchronization error signals to the origin with sufficient transient speed. Suitable adaptive laws of unknown parameters are designed that converged the estimated values of the unknown parameters to the true values of the systems parameters. Two numerical examples are presented and simulation results are derived to illustrate the effectiveness of the proposed dual synchronization approach.

MSC:

93C40 Adaptive control/observation systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C15 Control/observation systems governed by ordinary differential equations
34H10 Chaos control for problems involving ordinary differential equations
93B30 System identification
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