Class Of Time-delay Chaotic Systems Research Articles

The Synchronization of a Class of Time-Delayed Chaotic Systems Using Sliding Mode Control Based on a Fractional-Order Nonlinear PID Sliding Surface and Its Application in Secure Communication

A novel approach for the synchronization of a class of chaotic systems with uncertainty, unknown time delays, and external disturbances is presented. The control method given here is expressed by combining sliding mode control approaches with adaptive rules. A sliding surface of fractional order has been developed to construct the control strategy of the abovementioned sliding mode by employing the structure of nonlinear fractional PID (NLPID) controllers. The suggested control mechanism using Lyapunov’s theorem developed robust adaptive rules in such a way that the estimation error of the system’s unknown parameters and time delays tends to be zero. Furthermore, the proposed robust control approach’s stability has been demonstrated using Lyapunov stability criteria and Lipschitz conditions. Then, in order to assess the performance of the proposed mechanism, the presented control approach was used to simulate the synchronization of two chaotic jerk systems with uncertainty, unknown time delays, and external distortion. The results of the simulation confirm the robust and desirable synchronization performance. Finally, a secure communications mechanism based on the proposed technique is shown as a practical implementation of the introduced control strategy, in which the message signal is disguised in the transmitter with high security and well recovered in the receiver with high quality, according to the mean squared error (MES) criteria.

Synchronization of a Class of Uncertrain Time-Delay Chaotic Systems

Synchronization of a class of time-delay chaotic systems with parameters perturbation is discussed in this paper. The knowledge of the delay time is unknown. Firstly, we design a newresponse chaotic system , then based on Lyapunov-Krasovskii function, we show that the responsechaotic system can synchronize the driven system. The proposed method is tested and verified byan numerical example.

Adaptive unstable periodic orbit stabilization of uncertain time-delayed chaotic systems subjected to input nonlinearity

This paper investigates stabilizing the unstable periodic orbits (UPO) of uncertain time-delayed chaotic systems with sector nonlinearity in input function. The article proposes an adaptive output feedback control design based on the Lyapunov–Krasovskii approach, to stabilize the periodic solutions of a broad class of time-delayed chaotic systems, with unknown time-delay and uncertainty. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed method.

Different Types of Projective Synchronization in a Class of Time-Delayed Chaotic Systems Using Active Control Approach

We study different types of projective synchronization (projective-anticipating, projective, and projective-lag synchronization) in a class of time-delayed chaotic systems related to optical bistable or hybrid optical bistable devices. We relax some limitations of previous work, where the scaling factor α can not be any desired value. In this paper, we achieve projective-anticipating, projective, and projective-lag synchronization without the limitation of α. A suitable controller is chosen using active control approach. Based on the Lyapunov stability theory, we derive the sufficient stability condition through theoretical analysis. The analytical results are validated by the numerical simulations using Ikeda model and Mackey—Glass model.

A new delay-dependent synchronisation criterion for Lur e systems with delay feedback control

This paper considers the H? synchronisation of a class of time-delayed chaotic systems with external disturbance. Based on delay-dividing approach, a delay-dependent synchronisation condition is obtained by constructing a new Lyapunov functional, and one simulation example is given to show the effectiveness of the proposed chaos synchronisation scheme.

Synchronization and anti-synchronization of time-delay chaotic system and its application to secure communication

Based on Lyapunov stability theory and linear matrix inequality technique, the synchronization and anti- synchronization problem for a class of chaotic neural networks with delay was discussed, their own state feedback controller were presented, also the synchronization and anti-synchronization of this class of time-delay chaotic systems were realized in theory. Finally, this class of chaotic system was applied to secure communication, by system switching between the synchronization and anti-synchronization, a specific digital secure communication scheme was designed. The numerical simulation results verify the effectiveness of the method.

Lag synchronization of a class of chaotic systems with unknown parameters

Research on chaos synchronization of dynamical systems has been largely reported in literature. However, synchronization of different structure—uncertain dynamical systems—has received less attention. This paper addresses synchronization of a class of time-delay chaotic systems containing uncertain parameters. A unified scheme is established for synchronization between two strictly different time-delay uncertain chaotic systems. The synchronization is successfully achieved by designing an adaptive controller with the estimates of the unknown parameters and the nonlinear feedback gain. The result is rigorously proved by the Lyapunov stability theorem. Moreover, we illustrate the application of the proposed scheme by numerical simulation, which demonstrates the effectiveness and feasibility of the proposed synchronization method.

Formula omitted] synchronization of time-delayed chaotic systems

This paper considers H ∞ synchronization of a class of time-delayed chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the dynamic feedback controller is established to not only guarantee synchronization between derive and response systems, but also reduce the effect of external disturbance to an H ∞ norm constraint. Then, a criterion for existence of the controller is given in terms of LMIs. Finally, a numerical simulation is presented to show the effectiveness of the proposed chaos synchronization scheme.

Guaranteed cost control of time-delay chaotic systems via memoryless state feedback

Abstract This paper studies the problem of guaranteed cost control for a class of time-delay chaotic systems via memoryless state feedback. A design procedure is proposed to construct a memoryless state feedback controller, which guarantees that the resulting closed-loop system is asymptotically stable and achieves an adequate level of performance. A numerical example is provided to demonstrate the effectiveness of the proposed method.

Guaranteed cost control of time-delay chaotic systems

Abstract This article studies a guaranteed cost control problem for a class of time-delay chaotic systems. Attention is focused on the design of memory state feedback controllers such that the resulting closed-loop system is asymptotically stable and an adequate level of performance is also guaranteed. Using the Lyapunov method and LMI (linear matrix inequality) framework, two criteria for the existence of the controller are derived in terms of LMIs. A numerical example is given to illustrate the proposed method.

LMI optimization approach to stabilization of time-delay chaotic systems

Abstract Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, this paper proposes a novel control method for stabilization of a class of time-delay chaotic systems. A stabilization criterion is derived in terms of LMIs which can be easily solved by efficient convex optimization algorithms. A numerical example is included to show the advantage of the result derived.