Chaos synchronization using the Fourier series expansion with application to secure communications

In this paper, a new method for secure communication based on chaos synchronization is proposed. It is consisted of a state feedback controller and a robust control term using the Fourier series expansion for compensation of uncertainties. In comparison with other uncertainty estimators such as neural networks and fuzzy systems, Fourier series are more efficient, since they have fewer tuning. Thus, their tuning process is simpler. Similar to the parameters of fuzzy systems, Fourier series coefficients are estimated online using the adaptation rule obtained from stability analysis. The case study is the Duffing-Holmes oscillator. Also, observer-based secure communication using the Fourier series expansion has been proposed. Simulation results and comparisons, reveal the superiority of the proposed approach.