Finite-Time Synchronization of Fractional-Order Chaotic Systems with Different Structures under Stochastic Disturbances

Abstract

This paper studies the finite-time synchronization of fractional-order chaotic systems with different structures under parameter disturbance and external disturbance. We put forward a fractional-order controller that can achieve the finite-time synchronization of any-order fractional-order chaotic systems under stochastic disturbances. This controller has good robustness and anti-interference performance. With the concept of the finite-time stability theory given, some judgment criterions for the synchronization of fractional-order chaotic systems are proved. This method can not only make the error systems have a faster convergence rate but also can be implemented in engineering easily. The numerical simulations of two specific examples demonstrate the effectiveness of the method. At the same time, the synchronised time of finite-time synchronization is shorter and faster than the complete synchronization and the time can be adjusted according to the parameters in the controller.

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

“…References [11] designed a nonlinear adaptive control synchronization method for two identical Lorenz systems with unknown parameters. References [12][13] respectively researched the finite-time synchronization of integer order or fractional order of same dimensional chaotic systems with random disturbances and unknown parameters using the adaptive control method and Lyapunov stability theorem. These results show that the finite-time theorem is valuable in the synchronization control of uncertain chaotic systems and practical engineering.…”

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

“…A nonlinear adaptive control synchronization method is designed for two identical Lorenz systems with unknown parameters 11 . The finite-time synchronization of the integer and fractional order of a homogeneous chaotic system with random perturbations and unknown parameters is researched by using adaptive control methods and Lyapunov stability theorem in 12 , 13 . These results show that the finite-time theorem is valuable in the synchronization control of uncertain chaotic systems and practical engineering.…”