Adaptive control scheme for anti- synchronization of chaotic dynamical systems

Due to physical limitation in most real-world applications, the assumption on chaotic dynamical systems with identical drive and response systems is somehow unrealistic. Hence, synchronization of two different chaotic systems in the presence of unknown parameters is more essential and useful in real-world applications. Recently, several techniques have been proposed in the literature to synchronize chaotic dynamical systems. Therefore, this thesis presents chaos synchronization of a couple of chaotic systems. Based on the exponential and Lyapunov stability theory, the controller with the corresponding parameter update rules is designed such that the different chaotic systems can be synchronized asymptotically. The proposed function control is composed of both variable proportional and adaptive control actions for guaranteeing the convergence of the residual synchronization error to zero in the presence of disturbances. Three proposed chaos synchronization techniques are considered. The first technique considered chaos synchronization of two different chaotic systems with the same and different parametric perturbation by nonlinear control functions. Second technique studied an adaptive synchronization, phase synchronization and functional phase synchronization of two different chaotic systems with nonlinear control functions and the third technique, a robust adaptive nonlinear feedback controller technique is proposed to realize the synchronization between two different fractional order chaotic systems with fully unknown parameters, external disturbance and uncertainties. The proposed techniques are applied to achieve chaos synchronization for the chaotic dynamical systems We demonstrate that a coupled chaotic dynamical systems can be synchronized and numerical simulations show the effectiveness of the proposed control techniques. Moreover, as an application, a new technique for transmitting digital signals was proposed based on chaos masking using chaotic dynamical system. Also, simulation results verify the proposed technique’s success in the communication application.

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