Szász–Mirakyan-based adaptive controller design for chaotic synchronization

Abstract

This article presents a robust adaptive controller for chaos synchronization using the Szász–Mirakyan operator as a universal approximator. In accordance with the universal approximation theorem, the Szász–Mirakyan operator, an extended version of the Bernstein polynomial, can approximate uncertainties, including unmodeled dynamics and external disturbances. This fact is completely discussed in this article. It is shown that using the Szász–Mirakyan operator as basis functions and tuning the polynomial coefficients by the adaptive laws calculated in the stability analysis, uniformly ultimately bounded stability can be assured. Performance evaluation has also been carried out to confirm the satisfactory performance of transient response of the controller. Numerical simulations on the Duffing–Holmes oscillator are provided in order to demonstrate the effectiveness of this approach.