TITLE:
A Comparative Study of Synchronization Methods of Rucklidge Chaotic Systems with Design of Active Control and Backstepping Methods
AUTHORS:
Absana Tarammim, Musammet Tahmina Akter
KEYWORDS:
Chaotic System, Synchronization, Active Control, Backstepping Control, Lyapunov Function
JOURNAL NAME:
International Journal of Modern Nonlinear Theory and Application,
Vol.11 No.2,
June
29,
2022
ABSTRACT: The
performance of two widely used chaos synchronization approaches, active control
and backstepping control, is investigated in this study. These two methods are
projected to synchronize two chaotic systems (Master/Drive of Rucklidge
Systems) that are identical but have different initial conditions. The paper’s
significant feature is that based on error dynamics, controllers are designed
using the appropriate variable and the time synchronization between master
Rucklidge and drive Rucklidge systems using both methods. The control function
of the active control method is designed on the proper selection of matrices.
The chaotic behavior is controlled using a recursive backstepping design based
on the Lyapunov stability theory with a validated Lyapunov function. The
effectiveness of the controller in eradicating the chaotic behavior from the
state trajectories is also revealed using numerical simulations with Matlab.
The backstepping method is superior to the
active control method for synchronization of the measured pair of systems, as
it takes less time to synchronize while exhausting the first one than the
second one with great performance, according to numerical simulation and graphical
outcomes.