Synchronization Of Unified Chaotic System Research Articles

Secure Data Transmission Based on Adaptive Chattering-Free Sliding Mode Synchronization of Unified Chaotic Systems

This paper is concerned with a novel secure data transmission design based on adaptive synchronization of master and slave unified chaotic systems. First, by introducing an augmented error state, an adaptive continuous sliding mode control (SMC) is derived to guarantee the synchronization of unified chaotic systems. Then, the secret message embedded in the master chaotic system can be transmitted from transmitter to receiver. Different from previous works using discontinuous SMC, the undesired chattering phenomenon can be fully eliminated, and it becomes possible to precisely recover the embedded secret message at the receiver. Last, an example is given to illustrate the success of secure data transmission with the continuous SMC developed in this paper.

Synchronization of unified chaotic systems via adaptive nonsingular fast terminal sliding mode control

This paper investigates the robust synchronization problem for a class of unified chaotic systems with input nonlinearity via an adaptive nonsingular fast terminal sliding mode control. The proposed scheme not only ensures that the synchronization errors are fully derived to zero in the presence of system uncertainties and external disturbances, but also copes with the singularity and chattering phenomena. Using the adaptation laws, the estimation of unknown uncertainties and disturbances can be realized. The efficiency of the proposed scheme is verified in simulation results.

Finite-time hybrid projective synchronization of unified chaotic system

This paper presents finite-time hybrid projective synchronization for the unified chaotic system. The significant contribution of this paper is that master–slave system realizes hybrid projective synchronization within a pre-specified convergence time. Base on the Lyapunov stability theory and finite-time stability theory, a finite-time controller is derived to make the state of the slave system exponentially synchronize the state of the master system, and the different components of state of the slave system and the master system synchronize up to different desired scaling constant. Numerical simulations are presented to show the effectiveness of theoretical analysis.

Stabilization and Synchronization of Unified Chaotic System via Impulsive Control

The impulsive control and synchronization of unified chaotic system are proposed. By applying impulsive control theory and introducing a piecewise continuous auxiliary function, some novel and useful conditions are provided to guarantee the globally asymptotical stabilization and synchronization of unified chaotic system under impulsive control. Compared with some previous results, our criteria are superior and less conservative. Finally, the effectiveness of theoretical results is shown through numerical simulations.

Synchronization of unified chaotic system via adaptive wavelet cerebellar model articulation controller

This study aims to propose a more efficient control algorithm for the chaotic system synchronization. In this study, a novel wavelet cerebellar model articulation controller (WCMAC) is proposed, which incorporates the wavelet decomposition property with a cerebellar model articulation controller (CMAC). This WCMAC is a generalization network; in some special cases, it can be reduced to a wavelet neural network, a neural network and a conventional CMAC. Then, an adaptive wavelet cerebellar model articulation control system (AWCCS) is proposed to synchronize a unified chaotic system. In this AWCCS, WCMAC is the main controller utilized to mimic a perfect controller and the parameters of WCMAC are online adjusted by the derived adaptive laws; and a compensation controller is designed to dispel the residual of the approximation error for achieving $$ H^{\infty } $$ robust performance. The derived AWCCS is then applied to the chaotic system synchronization control. Finally, the effectiveness of the proposed control system is demonstrated through simulation results.

Generalized synchronization of bidirectionally coupled chaotic systems

This paper investigates the synchronization of Unified chaotic system and Rossler system via different methods. Several theorems for the synchronization of Unified chaotic system and Rossler system are deduced. Finally numerical simulation results are presented to show the feasibility and effectiveness of the approach. This synchronization method may be useful for sending secrete message and to understand synchronization of many biological systems, electronic circuits, chemical systems and potential applications to laser dynamics.

Synchronization of unified chaotic system by sliding mode/mixed H 2/H ∞ control

This paper deals with the synchronization of uncertain unified chaotic system in the presence of two kinds of disturbances, white noise and bounded power signal. A sliding mode controller (SMC) is established to guarantee the sliding motion. Moreover, a proportional-integral (PI) switching surface is used to determine the performance of the system in the sliding motion. Also, by using a mixed H 2/H ∞ approach, the effect of external disturbances on the sliding motion is reduced. The necessary parameters of constructing controller and switching surface are found via semidefinite programming (SDP) which can be solved effectively by a standard software. Finally, a numerical simulation is presented to show the effectiveness of the proposed method.

Sliding mode control design for generalized projective synchronization of unified chaotic systems containing nonlinear inputs

The problem of generalized projective synchronization for unified chaotic systems coupled with sector nonlinear inputs is investigated. Using the sliding mode control technique, a control scheme containing a new proportional–integral switching surface is developed to guarantee generalized projective synchronization even when the uncertainties and sector nonlinearity are present. Numerical simulations are included to demonstrate the effectiveness of the proposed synchronization scheme.

Chaos synchronization of unified chaotic systems via LMI

This Letter focuses on the master–slave synchronization problem of the unified chaotic systems. Based on Lyapunov stability theory and linear matrix inequality (LMI) formulation, a simple linear feedback control law is obtained to make the state of two identical unified chaotic systems asymptotically synchronized. Simulation results have illustrated the effectiveness of the proposed chaos synchronization solution.

Chaos control and synchronization of unified chaotic systems via linear control

Chaos control and synchronization in the unified chaotic systems is discussed in this paper. Based on the stability theory of a cascade-connected system, control laws are presented to achieve chaos control and synchronization, respectively. The advantage of the proposed controllers is that they are linear and have lower dimensions than that of the states. Simulation results for Lorenz, Lü and Chen chaotic systems are provided to illustrate the effectiveness of the proposed scheme.

Passivity‐Based Synchronization of Unified Chaotic System

This letter further improves and extends the work of Kemih et al. In detail, feedback passivity synchronization with only one controller for a unified chaotic system is discussed here. It is noticed that the unified system contains the noted Lorenz, Lu, and Chen systems. Numerical simulations are given to show the effectiveness of these methods.

Generalized projective synchronization of chaotic system based on a single driving variable and its application in secure communication

A generalized projective synchronization method is proposed based on unidirectional coupled synchronization by only transmitting a single driving variable. The proposed method allows us to arbitrarily direct the scaling factor to a desired value. Since chaos synchronization can be achieved by transmitting a single variable from driving system to response system, this method is more practical. Theoretical deduction and computer simulation show the effectiveness of the proposed method. A scheme for secure communication, which can increase the security of a communication system, is presented based on generalized projective synchronization of unified chaotic system.

Adaptive projective synchronization of unified chaotic systems and its application to secure communication

In this paper, a simple adaptive linear feedback control method is proposed for controlling the scaling factor between two coupled unified chaotic systems to a desired value, based on the invariance principle of differential equations. Under this control strategy, one can arbitrarily select the scaling factor. Numerical simulations are given to support the effectiveness of the proposed method and show the robustness against noise. Furthermore, a secure communication scheme based on the adaptive projective synchronization of unified chaotic systems is presented and numerical simulation shows its feasibility.

Synchronization of unified chaotic systems with uncertain parameters based on the CLF

Chaos synchronization in unified chaotic systems with uncertain parameters is discussed in this paper. On the basis of the control Lyapunov function (CLF), a feedback controller is designed which is only related to the boundaries of the uncertain parameters. Synchronization of two identical unified chaotic systems with different initial conditions is realized. Simulation results for Lorenz, Lü and Chen chaotic systems are provided to verify the effectiveness of the proposed scheme.

State-dependent Riccati equation synchronization method of unified chaotic system

Using improved state-dependent Riccati equation method，the state synchronization of unified chaotic systems is achieved. The state adjustors with given stability improve the dynamic performance of system synchronization. Theoretical deduction and simulation researches show that the error systems are asymptoticly stable. The comparative simulations with the traditional state-dependent Riccati equation method verify the improvement in dynamic performance of system synchronization.

Synchronization of unified chaotic system based on passive control

Chaos synchronization in the unified chaotic system was discussed using passive control. On the basis of the property of the passive system, the passive controller is designed and synchronization of two identical unified chaotic systems with different initial conditions is realized. Simulation results for two Lorenz, two Lü and two Chen chaotic systems are provided to show the effectiveness of the proposed synchronization method.

Robust synchronization of unified chaotic systems via sliding mode control

This paper investigates the chaos synchronization problem for a class of uncertain master–slave unified chaotic systems. Based on the sliding mode control technique, a robust control scheme is established which guarantees the occurrence of a sliding motion of error states even when the parameter uncertainty and external perturbation are present. Furthermore, a novel proportional–integral (PI) switching surface is introduced for determining the synchronization performance of systems in the sliding mode motion. Simulation results are proposed to demonstrate the effectiveness of the method.

Impulsive control, complete and lag synchronization of unified chaotic system with continuous periodic switch

Abstract The new unified chaotic system with continuous periodic switch between Lorenz and Chen systems is non-autonomous ones, which has many properties, such as symmetry and invariance, dissipative, tracking any target function etc. Control and synchronization of complete and lag for the system are discussed based on impulsive control theory in this paper. Some new general criteria for global asymptotical stability of continuous periodic switch system are established, and particularly some simple sufficient conditions are derived for stabilizing, complete and lag synchronizing chaotic system with continuous periodic switch. Theoretical analysis and numerical simulations are provided to show the effectiveness and feasibility of these methods.

On synchronization of unified chaotic systems via nonlinear Control

Abstract In this paper, a simple but efficient nonlinear control method is applied to the synchronization of unified chaotic systems using the Lyapunov method. A numerical example is given to illuminate the design procedure and advantage of the result derived.

Impulsive control and synchronization of unified chaotic system

We investigate the issue on impulsive control and synchronization of the unified chaotic system, which unifies both the Lorenz system and the Chen system. Some new and general conditions with varying impulsive distances are obtained to guarantee the impulsive control and synchronization global asymptotical stable. Especially, in the case of equal impulsive distances, some simple and easily verified sufficient conditions are derived for stabilizing and synchronizing the unified chaotic system. An illustrative example, along with computer simulation results, is finally included to visualize the effectiveness and feasibility of the developed methods.