Chaos synchronization using q-Chlodowsky operators as uncertainty approximator

Abstract

In this article, q-Chlodowsky operators are utilized for synchronizing a chaotic master-slave system. The universal approximation property enables q-Chlodowsky operators to approximate uncertainties, which consist of disturbances and unmodeled dynamics. It is verified that uniformly ultimately bounded stability of the tracking/approximation errors can be assured if the q-Chlodowsky operators are utilized as regressors and the polynomial coefficients are tuned by the adaptive laws calculated in the stability analysis. Moreover, it has been assumed that the rate of synchronization error is not at hand and a filter-based strategy has been adopted instead of designing an observer. The Duffing-Holmes oscillator is studied and the results are also compared with three powerful approximation-based and robust control methods. Unlike neural network/fuzzy estimators in which system states are necessary to define the regressor vector, the proposed uncertainty estimator does not require them in the regressor vector. Furthermore, in comparison with radial basis functions neural networks (RBFNNs), we are involved in fewer adaptive coefficients in the regressor vector of the proposed uncertainty estimator. As a result, the tedious and time-consuming procedure of trial and error for tuning the uncertainty estimator is eliminated.