توضیحات :
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.
