Bernstein-Schurer-Stancu operator–based adaptive controller design for chaos synchronization in the q-analogue

In this paper, a synchronization controller for chaotic master-slave systems is presented based on the q-analogue of the Bernstein-Schurer-Stancu operators. q-analogue of the Bernstein-Schurer-Stancu operators is employed to approximate uncertainties due to their universal approximation property. The coefficients of polynomials are considered free parameters and will be adjusted by the adaptive rules extracted from the stability analysis. Additionally, the controller is designed based on the presumption that the synchronization error rate is unavailable. The controller is applied on a master-slave system using Duffing-Holmes oscillators. The results are compared with the Radial Basis Function Neural Networks (RBFNN). Simulation results and comparisons show that the Bernstein-Schurer-Stancu operator in q-analogue is efficient in uncertainty approximation; needless, the system states for constructing the regressor vector and can be a good alternative for neural networks.