An application of Iterative Learning Control Theory (ILC) for system synchronization exhibited is in this study. The drive system is the Rossler system in this study is a macroscopic system. Another system is a mesoscopic system containing the resistive-capacitive-inductance shunted Josephson junctions (RCL-shunted JJ) to be the response system in this study. The ILC method is important to research for the robotics development in 1984. Many studies, such as image identification, adaptive control, sliding mode control and secure communication are gradually employed. The resistive-capacitive-inductance shunted Josephson junctions (RCL-shunted JJ) and resistive-capacitive shunted Josephson junctions (RCS JJ) are essentially nonlinear dynamical systems in a superconductor device could be used to synchronize drive-response system of chaos and chaos-based secure communication. The iterative error between the drive and response system influences the synchronization of systems. The Lyapunov criteria are still satisfied the mesoscopic, and the tracking error dynamics could be bounded and converged. There are also to exhibit system synchronized will be Lyapunov stable for which based on to designate appropriated learning the law. The simulation results demonstrate the consistent with the concept of proposing the controlled learning law and scheme.