A Comparative Study of Synchronization Methods of Rucklidge Chaotic Systems with Design of Active Control and Backstepping Methods  

作　　者：Absana Tarammim Musammet Tahmina Akter Absana Tarammim;Musammet Tahmina Akter(Department of Mathematics, Chittagong University of Engineering & Technology (CUET), Chattogram, Bangladesh)

机构地区：[1]Department of Mathematics, Chittagong University of Engineering & Technology (CUET), Chattogram, Bangladesh

出　　处：《International Journal of Modern Nonlinear Theory and Application》2022年第2期31-51,共21页现代非线性理论与应用（英文）

摘　　要：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.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.

关 键 词：Chaotic System SYNCHRONIZATION Active Control Backstepping Control Lyapunov Function 

分 类 号：O41[理学—理论物理]