Synchronization Of Discrete-time Chaotic Systems Research Articles

A Novel Event-Triggered Active Model Predictive Control for Synchronization of Discrete-Time Chaotic Systems

Abstract In this paper, synchronization of two identical discrete-time chaotic systems is considered in networked control environment where communication plays a significant role along with the synchronization performance. A new event-triggered (ET) active model predictive control (MPC) technique is proposed in the presence of constraints. With the help of active control, a linear MPC is sufficient to control a chaotic system. The active controller is not present all the time, rather only activated when a triggering condition is fulfilled. The MPC also solves the optimization problem only when an event is triggered. A triggering condition is designed to ensure a required performance bound. This technique reduces the computational burden as well as the frequency of communication between sensors and controller and controller and actuator. The effectiveness of the proposed scheme is illustrated by two simulation examples. A trade-off analysis between network traffic and synchronization performance, and its dependence on the prediction horizon is done for the considered system. It reveals that an optimum trade-off can be achieved according to the desired requirement.

Controlled synchronization of discrete-time chaotic systems under communication constraints

This paper investigates the controlled synchronization problem for a class of nonlinear discrete-time chaotic systems subject to limited communication capacity. A general chaotic master system and its slave system with a controller are connected via a limited capacity channel. In this case, the effect of quantization errors is considered. A practical quantized scheme is proposed so that the synchronization error is input-to-state stable with respect to the transmission error. Meanwhile, the transmission error decays to zero exponentially. This implies that the synchronization error converges to zero under a limited communication channel. A simulation example for the Fold chaotic system is presented to illustrate the effectiveness of the proposed method.

Impulsive synchronization of discrete-time chaotic systems under communication constraints

This paper investigates the problem of impulsive synchronization of discrete-time chaotic systems subject to limited communication capacity. Control laws with impulses are derived by using measurement feedback, where the effect of quantization errors is considered. Sufficient conditions for asymptotic stability of synchronization error systems are given in terms of linear matrix inequalities and algebraic inequalities. Some numerical simulations are given to demonstrate the effectiveness of the method.

Adaptive Function Projective Synchronization of Discrete Chaotic Systems with Unknown Parameters

Adaptive function projective synchronization of discrete-time chaotic systems with unknown parameters is considered. Based on the contraction mapping theorem, proper controllers and estimators are designed. Illustrative examples are provided to show the effectiveness of this method.

Function Projective Synchronization in Discrete-Time Chaotic System with Uncertain Parameters

The function projective synchronization of discrete-time chaotic systems is presented. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate function projective synchronization (FPS) of discrete-time chaotic systems with uncertain parameters. With the aid of symbolic-numeric computation, we use the proposed scheme to illustrate FPS between two identical 3D Hénon-like maps with uncertain parameters. Numeric simulations are used to verify the effectiveness of our scheme.

Adaptive Control and Function Projective Synchronization in 2D Discrete-Time Chaotic Systems

This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discrete-time chaotic systems. In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems. Numerical results demonstrate the effectiveness of the proposed control scheme.

An improved harmony search algorithm for synchronization of discrete-time chaotic systems

The harmony search (HS) algorithm is a recently developed meta-heuristic algorithm, and has been very successful in a wide variety of optimization problems. HS was conceptualized using an analogy with music improvisation process where music players improvise the pitches of their instruments to obtain better harmony. The HS algorithm does not require initial values and uses a random search instead of a gradient search, so derivative information is unnecessary. Furthermore, the HS algorithm is simple in concept, few in parameters, easy in implementation, imposes fewer mathematical requirements, and does not require initial value settings of the decision variables. In recent years, the investigation of synchronization and control problem for discrete chaotic systems has attracted much attention, and many possible applications. The tuning of a proportional–integral–derivative (PID) controller based on an improved HS (IHS) algorithm for synchronization of two identical discrete chaotic systems subject the different initial conditions is investigated in this paper. Simulation results of the IHS to determine the PID parameters to synchronization of two Hénon chaotic systems are compared with other HS approaches including classical HS and global-best HS. Numerical results reveal that the proposed IHS method is a powerful search and controller design optimization tool for synchronization of chaotic systems.

Novel synchronization of discrete-time chaotic systems using neural network observer

This paper presents a new approach to solve the synchronization problem of a large class of discrete chaotic systems. The chaotic systems can be reformulated as an appropriate class of linear parameter varying (LPV) systems. The synchronization problem for this class of nonlinear systems is revisited from a control perspective and it is argued that the problem can be viewed as an observer design problem. Then, based on the LPV representation, a neural network observer-based approach is proposed to solve the synchronization problem. The simulation results show the advantages of combining the LPV techniques and the neural networks to determine the appropriate observer gain within the context of chaotic system synchronization.

Function Projective Synchronization of Discrete-Time Chaotic Systems

First, a function projective synchronization is defined in discrete-time dynamical systems, in which the drive and response state vectors evolve in a proportional scaling function matrix. Second, based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discrete-time chaotic systems. With the aid of symbolic-numeric computation, we use the proposed scheme to illustrate the function projective synchronization between the 2D Lorenz discrete-time system and the Fold discrete-time system, as well as between the 3D hyperchaotic Rössler discrete-time system and the Hénon-like map. Numeric simulations are used to verify the effectiveness of our scheme. By choosing different scaling functions, the interesting attractor figures of the drive and response systems are showed in a proportional scaling function.

Observer-based synchronization of discrete-time chaotic systems under communication constraints

The paper is devoted to the synchronization problem of the discrete-time chaotic systems, coupled by the link (“the communication channel“) with the limited bit-per-step rate. The observer-based full-order coder is designed, ensuring decay of the synchronization error asymptotically for the case when channel imperfections and computation errors are neglected. It is shown that if the computations in the both master and slave nodes of the channel are identical, the synchronization error can be made close to the maximum achievable accuracy of the given computer depending only on the number of digits in the computer (practical synchronization). If the calculations in the coder and decoder are not identical (e.g., if the computers on these nodes have different number of digits), after the some time interval of decreasing the synchronization error, the mis-synchronization occurs due to unstable properties of the chaotic systems. For this case, the practical synchronization may be ensured applying the fixed-point arithmetic calculations.The result is illustrated numerically on the example of synchronization chaotic Hénon systems.

A New Approach to Synchronization of Discrete-Time Chaotic Systems

This letter deals with the synchronization of discrete-time chaotic systems. Based on the Lyapunov method, we present a new control method that guarantees that the synchronized states are asymptotically stable. The controller consists of two parts: one is a linear dynamic controller, and the other is a nonlinear control law for compensating the nonlinear terms of the error signal. Then, the existence criterion of the controller for the synchronization is derived. The criterion is expressed as a linear matrix inequality (LMI), readily solvable by various convex optimization algorithms.

Generalized (complete, lag, anticipated) synchronization of discrete-time chaotic systems

A unify definition of generalized (complete, lag, anticipated) synchronization in discrete-time chaotic systems is proposed in this paper. Based on the contraction mapping theorem, a new general scheme is proposed for the generalized synchronization of discrete-time chaotic and hyper-chaotic systems. The well-known Hénon mapping and generalized hyper-chaotic Hénon mapping are chosen to illustrate the proposed scheme. Numerical simulations are also shown to verify the effectiveness of the proposed control method.

Adaptive fuzzy synchronization of discrete-time chaotic systems

Abstract This paper presents a fuzzy model-based adaptive approach to synchronize two different discrete-time chaotic systems. Takagi–Sugeno (TS) fuzzy model is employed to represent the chaotic drive and response systems. Since the parameters of the drive system are assumed unknown, an adaptive law is derived to estimate its unknown parameters. Then, a control law is proposed to stabilize the error dynamics. The design procedure is illustrated by two examples to demonstrate the effectiveness of the proposed methodology.

Chaos communication based on synchronization of discrete-time chaotic systems

A novel chaos communication method is proposed based on synchronization of discrete-time chaotic systems. This method uses a full-order state observer to achieve synchronization and secure communication between the transmitter and the receiver. Further, we present a multiple-access chaotic digital communication method by combining the observer with the on-line least square method. Simulation results are also given for illustration.

Synchronization of generalized Henon map via backstepping design

Abstract This paper proposes a backstepping method to resolve the synchronization of discrete-time chaotic systems. The proposed scheme offers systematic design method for the synchronization of a class of discrete-time hyper-chaotic systems, which implies much complicated high-order chaotic systems can be used to improve the security in chaos communications. A well-known chaotic systems: generalized Henon map is considered as illustrative example to demonstrate the general applicability of backstepping design. Numerical simulations verify the effectiveness of the approach.

Control and synchronization of discrete-time chaotic systems via variable structure control technique

We present an input/output linearization control method incorporated in a discrete-time variable structure control technique to resolve the output tracking problem of a class of discrete-time nonlinear systems. The proposed control scheme is then applied to address the control and synchronization problems associated with the Hénon chaotic systems. Numerical simulations demonstrate the feasibility and robustness of the proposed control strategy.