Chaos synchronization using differential equations as extended state observer

Abstract

In this paper, an extended state observer (ESO) is presented for synchronizing a chaotic master-slave system based on linear differential equations. The universal approximation property enables linear differential equations to estimate uncertainties, consisting of disturbances and unmodeled dynamics. The main contribution of this study is developing a control scheme based on ESO, which is designed using differential equations. In other words, an Nth-order linear differential equation is utilized to model the lumped uncertainty. The controller is proposed based on a model-free approach to eliminate the need for accurate information from the system model and assure a robust tracking performance. Furthermore, a thorough mathematical analysis is given based on the Lyapunov stability theorem to confirm the uniform ultimate boundedness of the observation/tracking approximation errors. To analyze the performance of the ESO-controller scheme in terms of transient response behavior and robustness, the Duffing-Holmes oscillator is considered as the simulation testbed. A set of five different experiments are conducted to evaluate the efficiency of the introduced control approach. The results of ESO are also compared with two powerful approximation methods.