Synchronization and Anti-Synchronization of Two Identical Hyperchaotic Systems Based on Active Backstepping Design

This paper presents an active backstepping design method for synchronization and anti-synchronization of two identical hyperchaotic Chen systems. The proposed control method, combining backstepping design and active control approach, extends the application of backstepping technique in chaos control. Based on this method, different combinations of controllers can be designed to meet the needs of different applications. Numerical simulations are shown to verify the results

Synchronization and antisynchronization protocol design of chaotic nonlinear gyros: an adaptive integral sliding mode approach

A novel control protocol design, via integral sliding mode control with parameter update laws, for synchronization and desynchronization of a chaotic nonlinear gyro with unknown parameters is the focus of this work. The error dynamics of the actual system are substructured into nominal and uncertain parts to employ adaptive integral sliding mode (AISM) control. The uncertain parameters are estimated via devised adaptive laws. Then the disagreement dynamics are guided to origin via AISM control. The stabilizing controller is also designed in terms of nominal control along with a compensating component. The control and the parameter update laws are constructed to ensure the strictly negative derivative of a Lyapunov function. Graphical results related to synchronization, desynchronization, and chaos suppression are displayed to demonstrate the potential of the proposed control

Projective synchronization of chaotic systems via backstepping design

Abstract Chaos synchronization of discrete dynamical systems is investigated. An algorithm is proposed for projective synchronization of chaotic 2D Duffing map and chaotic Tinkerbell map. The control law was derived from the Lyapunov stability theory. Numerical simulation results are presented to verify the effectiveness of the proposed algorithm</jats:p

Adaptive Projective Lag Synchronization of T and Lu Chaotic Systems

In this paper, the synchronization problem of T chaotic system and Lu chaotic system is studied. The parameter of the drive T chaotic system is considered unknown. An adaptive projective lag control method and also parameter estimation law are designed to achieve chaos synchronization problem between two chaotic systems. Then Lyapunov stability theorem is utilized to prove the validity of the proposed control method. After that, some numerical simulations are performed to assess the performance of the proposed method. The results show high accuracy of the proposed method in control and synchronization of chaotic systems

Control and synchronization of the generalized Lorenz system with mismatched uncertainties using backstepping technique and time‐delay estimation

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140007/1/cta2353.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/140007/2/cta2353_am.pd

Generalized Synchronization with Uncertain Parameters of Nonlinear Dynamic System via Adaptive Control

An adaptive control scheme is developed to study the generalized adaptive chaos synchronization with uncertain chaotic parameters behavior between two identical chaotic dynamic systems. This generalized adaptive chaos synchronization controller is designed based on Lyapunov stability theory and an analytic expression of the adaptive controller with its update laws of uncertain chaotic parameters is shown. The generalized adaptive synchronization with uncertain parameters between two identical new Lorenz-Stenflo systems is taken as three examples to show the effectiveness of the proposed method. The numerical simulations are shown to verify the results

Chaos Synchronization Using Active Control and Backstepping Control: A Comparative Analysis

This paper examines the synchronization performance of two widely used&nbsp;chaos synchronization techniques: active control and backstepping control. It is shown&nbsp;that the two methods have excellent performance, with the active control marginally&nbsp;outperforming the backstepping control in terms of transient analysis. However, the&nbsp;complexity of active controllers suggests that the backstepping control would be more&nbsp;attainable in engineering applications