Synchronization of a class of uncertain chaotic systems utilizing a new finite-time fractional adaptive sliding mode control

Abstract

This paper mainly focuses on the issue of finite-time synchronization of a class of chaotic master and slave systems when they have uncertainties, disturbances, and unknown parameters. It is supposed that Uncertainties and disturbances bounds are unknown. First, using the concept of fractional calculus, a new fractional sliding surface is proposed and its finite-time convergence is also proved. Second, appropriate adaptive laws are introduced to overcome unknown system parameters and these laws correctly estimate the unknown values. With applying the controller, synchronization is achieved within a short time. Also after the synchronization, unstable fluctuations are removed and the controlled system has perfect robustness. The proposed approach is applicable to a wide range of identical or non-identical chaotic master and slave systems. Theoretical analysis and stability examination of the proposed method have been performed utilizing adaptive methods and Lyapunov stability theorem. Thereafter, two practical examples are presented to evaluate the effectiveness and usefulness of the suggested method. Furthermore, this method is compared with methods in recent articles, which shows the superiority of this method.