Finite-time synchronization of different dimensional chaotic systems with uncertain parameters and external disturbances

Abstract

This paper proposes a new control scheme using two scaling matrices that realizes the finite-time synchronization of different-dimensional chaotic systems with parameter uncertainties and external disturbances. Firstly, based on Lyapunov stability theorem and finite-time stability theorem, the definition of finite-time synchronization of chaotic systems with different dimensions is introduced. Secondly, in the case of external disturbance and parameter uncertainty, an adaptive feedback hybrid controller and parameter adaptive laws are designed to synchronize different dimensional uncertain chaotic systems in finite-time. Then, according to the characteristics of the unknown parameters of the system, a transformation matrix is constructed to meet the needs of chaotic systems with different dimensions, and a simplified synchronization control scheme is designed. Finally, two numerical experiments are carried out to verify the effectiveness of the proposed methods.

Finite-Time Synchronization of the Rabinovich and Rabinovich-Fabrikant Chaotic Systems for Different Evolvable Parameters

“…Finite-time schemes are realized with the application of Lyapunov stability criteria in conjunction with definitions and lemmas. In recent years, finite-time control and synchronization schemes have attracted much attention they have been applied to the synchronization of chaotic systems with different dimensions and uncertainties [34]- [36], coronary artery chaotic systems [37], memristor chaotic systems [38] and hyperchaotic systems [33] amongst others. In this section, we summarized a body of definitions and lemmas suitable for the synchronization of the Rabinovich and Rabinovich-Fabrikant systems.…”