Controller Parameter Optimization for the Robust Synchronization of Chaotic Systems with Known and Unknown Parameters

In this paper, a synchronization problem of a three-dimensional (3-D) Coullete chaotic system using the active- and adaptive-based synchronization control techniques is addressed. Based on the Routh-Hurwitz criterion and using the active control algorithm, a single control function is considered and a computational study is performed to identify the correct balance between the converging rates of the synchronization error signals to the origin and magnitude of the linear controlling parameters (LCPs) for the globally exponential synchronization (GES) between two identical 3-D Coullete chaotic systems. In order to achieve the complete synchronization (CS) objective with unknown model uncertainties, external disturbances, and unknown time-varying parameters, a novel nonlinear adaptive synchronous controller is proposed and suitable adaptive laws of time-varying parameters are designed that accomplish the asymptotic synchronization between two identical uncertain 3-D Coullete chaotic systems. The two synchronizing controlling approaches are applied to investigate the CS phenomenon, and the results are compared. Open research problems are also discussed. All simulations results are carried out to validate the effectiveness of the proposed synchronization control approaches by using Mathematica 10.0.