Behavior learning of a memristor-based chaotic circuit by extreme learning machines

Abstract

As the behavior of a chaotic Chua's circuit is nonstationary and inherently noisy, it is regarded as one of the most challenging applications. One of the fundamental problems in the prediction of the behavior of a chaotic Chua's circuit is to model the circuit with high accuracy. The current paper presents a novel method based on multiple extreme learning machine (ELM) models to learn the chaotic behavior of the four elements canonical Chua's circuit containing a memristor instead of a nonlinear resistor only by using the state variables as the input. In the proposed method four ELM models are used to estimate the state variables of the circuit. ELMs are first trained by using the data spoilt by noise obtained from MATLAB models of a memristor and Chua's circuit. A multistep-ahead prediction is then carried out by the trained ELMs in the autonomous mode. All attractors of the circuit are finally reconstructed by the outputs of the models. The results of the four ELMs are compared to those of multiple linear regressors (MLRs) and support vector machines (SVMs) in terms of scatter plots, power spectral density, training time, prediction time, and some statistical error measures. Extensive numerical simulations results show that the proposed system exhibits a highly accurate multistep iterated prediction consisting of 1104 steps of the chaotic circuit. Consequently, the proposed model can be considered a promising and powerful tool for modeling and predicting the behavior of Chua's circuit with excellent performance, reducing training time, testing time, and practically realization probability.