Abstract
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.
Highlights
The method of Iterative Learning Control (ILC) was applied to mechanical robots in 1984 for performance improvement
The ILC theory was employed for chaos synchronization to stabilize communication protocols of encrypting and decrypting a message using dynamical filters, which are bi-directional over unidirectional coupling schemes of Bernoulli units, towards the tap-proof transmission of information via chaotic laser systems [5,6]
ILC was employed for dynamical system synchronization based on classical linear system theory [8,9,10,11]
Summary
The method of Iterative Learning Control (ILC) was applied to mechanical robots in 1984 for performance improvement. The improvement is made possible by designing an on-line iterative learning scheme based on a classical linear system that approximates well the original nonlinear system of the robots The approach of this on-line-learning ILC is very different from other known approaches, such as repetitive control, adaptive control, and the neural network [1,2]. The essence of on-line learning lies in the attribute of the controller that adapts its controller effort continuously based on the error feedback from the output of the system in an on-line fashion [2,3,4] This ILC control method is applicable to many industrial systems for manufacturing, robotics, and assembly line in mass production [2,3]. This paper derives a conclusion and a recommendation for future works
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