Adaptive observer-based synchronization of two non-identical chaotic systems with unknown parameters

In this study, adaptive observer-based synchronization of chaotic systems is considered. The master and slaves systems have different dynamics and it is assumed that the master system parameters are unknown while its states are available. First, it is assumed that the slave system parameters are known but its states are not completely available. It is shown that an observer for the slave system can be designed and applied for the purpose of synchronization. Based on a Lyapunov function, an adaptive law for master parameters estimation and a control law for the synchronization goal are extracted. Stability of the entire system including the observer dynamics has been proved. Further, it is assumed that the parameters of both master and slave systems are unknown. For this case, an adaptive nonlinear observer is designed to estimate the slave system states and two adaptive laws for estimating the unknown parameters are proposed. In addition, a proper control law to achieve the synchronization goal has been suggested, and the stability of the closed-loop system is established. Finally, the effectiveness of the proposed synchronization method is shown via simulation results.