Observer-based adaptive controller design for chaos synchronization using Bernstein-type operators

This article uses the Bernstein-type operators as the universal approximator to present an observer-based robust adaptive controller for chaos synchronization. The lumped uncertainties including, un-modeled dynamics and external disturbances, are modeled with this potent mathematic tool. It is shown that using the Bernstein-type operators as basis functions and tuning the polynomial coefficients by the adaptive laws calculated in the stability analysis, uniform ultimate boundedness of the observer estimation error and synchronization error can be assured. To analyze the performance of the proposed controller scheme in terms of transient response behavior and robustness, the Duffing-Holmes oscillator is considered as the simulation testbed. A set of two different experiments are conducted to evaluate the efficiency of the introduced control approach. The performance of the proposed approach is also compared with RBFNN as a powerful approximation method. Unlike neural network/fuzzy methods, which require system states as inputs to estimate functions and construct a regressor vector, the proposed method is not dependent on the system states. Furthermore, there are more adjustable parameters in the regressor vector of the RBFNN (such as the width and center of the Gaussian units), and assigning the best values for these parameters is tedious and time-consuming work due to the repeated trial and error.

Automated summary

This article presents an observer-based robust adaptive controller for chaos synchronization using Bernstein-type operators. It shows that this method can assure the uniform ultimate boundedness of the observer estimation error and synchronization error. The performance of the proposed approach is evaluated using the Duffing-Holmes oscillator and compared with RBFNN.