Synchronization of a Novel Class of Fractional-Order Uncertain Chaotic Systems via Adaptive Sliding Mode Controller

Abstract

In this work an adaptive sliding mode controller in the presence of uncertainty, as well as the external disturbance is considered. A concise introduction and investigation of the dynamic behavior of a novel class of chaotic systems with fractional order derivatives for synchronization is presented. It is supposed that the high bounds of uncertainty and external disturbance are unknown. The proposed controller is designed based on error dynamics and acceptable adaptive laws. The sliding mode dynamic stability and the condition to start sliding are proved by Lyapunov stability theory. With this new proposed approach, Chen and Lorenz system with fractional order derivatives are synchronized. Finally, simulation results with MATLAB software showed that the designed comparative sliding mode controller was able to synchronize chaotic systems with fractional order derivatives in the presence of the mentioned adverse factors. The main characteristic of the proposed method compared to other methods is providing acceptable adaptive laws for satisfactory functioning against uncertainty and external disturbance and eliminate the chattering phenomenon for synchronization of non-identical chaotic systems with fractional order derivatives.