Adaptive Unknown-Input Observers-Based Synchronization of Chaotic Systems for Telecommunication

We propose a robust adaptive chaotic synchronization method based on unknown-input observers for master-slave synchronization of chaotic systems, with application to secured communication. The slave system is modelled by an unknown input observer in which, the unknown input is the transmitted information. As in the general observer-based synchronization paradigm, the information is recovered if the master and slave systems robustly synchronize. In the context of unknown-input observers, this is tantamount to estimating the master´s states and the unknown inputs. The set-up also considers the presence of perturbations in the chaotic transmitter dynamics and in the output equations (the transmitted signal). That is, the estimator (slave system) must synchronize albeit noisy measurements and reject the effect of perturbations on the transmitter dynamics. We provide necessary and sufficient conditions for synchronization to take place. To highlight our contribution, we also present some simulation results with the purpose of comparing the proposed method to classical adaptive observer-based synchronization (without disturbance rejection). It is shown that additive noise is perfectly canceled and the encoded message is well recovered despite the perturbations.