Preprint Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 1 November 2017 / Approved: 1 November 2017 / Online: 1 November 2017 (05:45:02 CET)

A peer-reviewed article of this Preprint also exists.

Cheng, C.-K.; Chao, P.C.-P. Chaotic Synchronizing Systems with Zero Time Delay and Free Couple via Iterative Learning Control. Appl. Sci. 2018, 8, 177. Cheng, C.-K.; Chao, P.C.-P. Chaotic Synchronizing Systems with Zero Time Delay and Free Couple via Iterative Learning Control. Appl. Sci. 2018, 8, 177.

Journal reference: Appl. Sci. 2018, 8, 177
DOI: 10.3390/app8020177

Abstract

This research not only dedicated a less restrictive method of iteration-varying function for a learning control law to design a controller but also synchronize two nonlinear systems with free time-delay. In addition, the mathematical theory of system synchronization has proved rigorously and the theory verified through an example to demonstrate the behavior of each parameter in the theory. The design of a controller using the iterative learning control law is significant for robotic tracking. The controller in this research generates a feed-forward control input using the error dynamics among the drive-response systems. The error dynamics satisfies the Lyapunov function and the combination of output errors, which respectively represented relative estimated differences of the drive-response systems. The iterative learning control rule serves the function of a filter adding previous control error after the end of each iteration. The numerical example of a synchronous system is given a Lorenz system for driving and another with the iterative learning control law for response under different initial condition. The results verify and demonstrate the proposed mathematical theory. The simulation exhibits consistency in the behavior of each parameter to match mathematical theory.

Subject Areas

synchronization; chaos; chaotic system; Iterative Learning Control (ILC); Lyapunov function; error convergent

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