Adaptive Control and Synchronization of a New Three-Dimensional Chaotic System with Uncertain Parameters

Abstract

In this paper, we address chaos control and synchronization problems of a new 3D chaotic system with uncertain parameters. Based on the Lyapunov stability theory and adaptive theory, the adaptive control law is derived such that the trajectory of the new chaotic system with unknown parameters can be globally stabilized to an unstable equilibrium point of the uncontrolled system. Meanwhile, an adaptive control approach is presented to the synchronization between two identical new uncertain chaotic systems. It is shown in detail that the chaos control and synchronization phenomena of this new uncertain 3D chaotic system can be realized by designing suitable adaptive control laws and parameter estimation update laws. In addition, numerical examples are presented to illustrate the feasibility and effectiveness of the theoretical analysis.