Chaos synchronization in RCL-shunted Josephson junction via active control

Trajectory Tracking between Josephson Junction and Classical Chaotic System via Iterative Learning Control

“…In this research, the ILC tracking method has been applied to the Josephson junction chaos. Many studies providing other methods such as the backstepping controller [7], the active control [8], common chaos driving by Rossler [9], and LMI [16] should show similar demonstrations.…”

“…A non-linear controller by utilizing the back-stepping technique has been investigated to control bifurcation in the RCLs-JJ system [7]. The chaos synchronization between two identical RCLs-JJ systems has been examined in which a number of different techniques to design the controller such as using active control [8], utilizing a common chaos to drive RCLs-JJ system approaching synchronization [9], applying the back-stepping [10][11][12][13], and using the time-delay feedback control [14], respectively. In other studies, the controller design or controller rule is directly determined by the Lyapunov function [11,12] and the RCLs-J junctions array synchronization [12].…”

A Research on Active Control to Synchronize a New 3D Chaotic System

“…Lei et al [14] reported the synchronization problem of two identical nonlinear gyros using the active control based on the Routh-Hurwitz criterion and Lyapunov stability theory. Ucar et al [15] utilized the active control technique for chaos synchronization in RCL-shunted Josephson function. Njah and Vincent [16] investigated the synchronization and anti-synchronization of two identical extended BVP chaotic oscillators by using the generalized active control method.…”

“…However, the finding of these studies [10,[13][14][15][16][17] guarantee the asymptotic stability of the resulting synchronization error dynamics by allocating negative eigenvalues of the coefficient matrix in the closed-loop system that simply obeys the Routh-Hurwitz criterion. Convergence rates of the synchronization error signals depend on the numeric values of the controller gain coefficients.…”

“…In real-life applications, selecting high controller gain coefficients may lead to automatic signal saturations and the two coupled chaotic/hyperchaotic systems may lose synchronization stability completely. In fact, the above notable results [10,[13][14][15][16][17] affect each other mutually and need a systematic approach to compute suitable linear controller gains. In addition, the chaotic systems are considered free of the unknown external disturbance.…”