Design of nonlinear observer for chaotic message transmission

Abstract

Chaos is an interesting nonlinear phenomena that occurs in wide variety of fields. A significant amount of research was devoted to understanding chaos and its properties. After that, researchers focused on searching for possible application areas for chaos to utilize its properties. The need to increase the security of a communication system is considered as a perfect match for chaos and its several properties, yielding chaotic communication. In this thesis, chaotic communication is approached from a control theory perspective. Specifically, three nonlinear observers are designed to extract message encrypted in a chaotic communication signal. The design and stability analysis is presented for the first observer, and the other observers are presented as modifications to the first one. Extensive numerical simulations are performed to demonstrate the viability of the proposed observers. Robustness of the observers to noise, additive disturbances, and parametric mismatch, and security of the observers are demonstrated numerically.