Finite-time synchronization between two different chaotic systems with uncertainties

TL;DR

This paper introduces a novel adaptive control method using virtual unknown parameters to achieve finite-time synchronization of two different chaotic systems with uncertainties, avoiding direct dependence on unknown parameters.

Contribution

It proposes a new virtual unknown parameter approach for finite-time synchronization of different chaotic systems with uncertainties, applicable with single or multiple virtual parameters.

Findings

Successfully synchronizes two different chaotic systems in finite time

The method handles unknown parameters and disturbances effectively

Numerical simulations validate the approach

Abstract

A new method of virtual unknown parameter is proposed to synchronize two different systems with unknown parameters and disturbance in finite time. Virtual unknown parameters are introduced in order to avoid the unknown parameters from appearing in the controllers and parameters update laws when the adaptive control method is applied. A single virtual unknown parameter is used in the design of adaptive controllers and parameters update laws if the Lipschitz constant on the nonlinear function can be found, while multiple virtual unknown parameters are adopted if the Lipschitz constant cannot be determined. Numerical simulations show that the present method does make the two different chaotic systems synchronize in finite time.