Robust Polynomial Observer-Based Chaotic Synchronization for Non-ideal Channel Secure Communication: An SOS Approach

摘要

This paper proposes a novel chaotic-based secure communication scheme for non-ideal transmitting public channel. The proposed approach employs a polynomial model and sum-of-squares (SOS) decomposition technique to synchronize chaotic transmitter and receiver systems. Because of high secure communication demands and practical limitations in transforming the signals on the public channel, only limited information of the transmitter system is transformed. Therefore, at the receiver side, a robust polynomial observer-based controller is proposed to estimate the states of the transmitter and synchronize the chaotic systems. Also, since the channel is noisy and non-ideal, H_∞ performance criterion is used and the sufficient design conditions of controller and observer are derived in terms of SOS decomposition such that the information is effectively recovered in the presence of external disturbances and noisy environment. In addition, to further remove the effect of the noise on the information recovery, a Savitzky-Golay polynomial filter is utilized. Finally, to show the effectiveness of the proposed approach, two chaotic and hyperchaotic case studies are considered and the obtained results are compared with the existing ones.