Class Of Discrete Chaotic Systems Research Articles

Set-stabilization of discrete chaotic systems via impulsive control

In this letter, for the first time, set-stabilization is addressed for a class of discrete chaotic systems by using impulsive control. By using the Lyapunov stability theory and algebraic inequality techniques, some sufficient conditions for global exponential set-stability of the impulsive controlled discrete chaotic systems are obtained and the attracting set of the systems is also given. It is shown that not only a discrete chaotic system but also an unbounded discrete system can be successfully set-stabilized by impulses. The numerical simulation on the Lozi discrete chaotic system is presented to illustrate the effectiveness of the obtained results.

Adaptive Feedback Control for a Class of Discrete Chaotic Systems

Discrete chaotic systems are more difficult to control than continuous chaotic systems. We discuss adaptive control scheme of continuous chaotic systems published in a series of papers, and study on how the convergence factor affects the convergence time and the property of final control strength by mathematical analysis and number simulations. Then we generalize it into discrete systems satisfying certain conditions and provide mathematical proof. The effect of convergence factor is emphasized. Finally, we apply the scheme to two discrete chaotic systems, which verify its effectiveness.

Improved piece-wise linear and nonlinear synchronization of a class of discrete chaotic systems

This paper deals with the chaotic synchronization of a discrete chaotic system. Based on a stable analysis, improved piece-wise linear feedback and nonlinear feedback control methods were given. Both the methods can achieve chaotic synchronization efficiently with one control input. The range of coupling coefficient is calculated in both the methods. Compared with nonlinear controls, the improved piece-wise linear controls have simpler structures and can be obtained more easily. Finally, the numerical simulation results verified the effectiveness of both the methods.

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.

A Neural Network Observer-Based Approach for Synchronization of Discrete-Time Chaotic Systems

This paper presents a new approach to solve 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. 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.

RADIAL BASIS FUNCTION NETWORKS AS CHAOTIC GENERATORS FOR SECURE COMMUNICATION SYSTEMS

This paper improves upon a new class of discrete chaotic systems (i.e. chaotic maps) recently introduced for effective information encryption. The nonlinearity and adaptability of these systems are achieved by designing proper radial basis function networks. The potential for automatic synchronization, the lack of periodicity and the extremely large parameter spaces of these chaotic maps offer robust transmission security. The Radial Basis Function (RBF) networks offer a large number of parameters (i.e. the centers and spreads of the RBF kernels and the weights of the linear layer) while at the same time as universal approximators they have the flexibility to implement any function. The RBF networks can learn the dynamics of chaotic systems (maps or flows) and mimic them accurately by using many more parameters than the original dynamical recurrence. Since the parameter space size increases exponentially with respect to the number of parameters, the RBF based systems greatly outperform previous designs in terms of encryption security. Moreover, the learning of the dynamics from data generated by chaotic systems guarantees the chaoticity of the dynamics of the RBF networks and offers a convenient method of implementing any desirable chaotic dynamics. Since each sequence of training data gives rise to a distinct RBF configuration, theoretically there exists an infinity of possible configurations.