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This study aims to orchestrate a less restrictive learning controller by using the iteration-varying function, the so-called iterative learning controller (ILC), to synchronize two nonlinear systems with free time delay and couple free. The mathematical theories are proven rigorously and controllers are developed for system synchronization, and then an example is forged to demonstrate the effectiveness of synchronization by the designed ILC. The ILC is designed with a feed-forward based by the error dynamics between the two considered nonlinear drive and response systems. The stability of the synchronization facilitated by the designed ILC is ensured by rendering the convergence of an error dynamics that satisfied the Lyapunov function. The Lorenz system within a drive-response system is considered as one system that drives another for the demonstration of the effectiveness of the designed ILC to achieve synchronization and verified initial conditions. Simulations are conducted for the controlled Lorenz system, and the results validated well the expected capability of the designed ILC for synchronization and matched the proposed mathematical theory.

Chaotic Synchronizing Systems with Zero Time Delay and Free Couple via Iterative Learning Control