Chaos Synchronization by Model Reference Adaptive Control Using Fixed Point Transformations

In this paper a special Model Reference Adaptive Controller (MRAC) is suggested for the synchronization of the signals two Chua circuits of significantly different parameters in the chaotic regime of their motion. One of the circuits has exactly known parameters. This system provides the trajectory that has to be traced by the other circuit the parameters of which are unknown. The known circuit also serves as the reference model the dynamic behavior of which has to be imitated by the controlled system for the external control loop. In contrast to the traditional approaches that normally apply Lyapunov’s direct method for designing the controller the suggested method applies Robust Fixed Point Transformations (RFPT) that is far simpler design technique. The results of computer simulations clearly reveal that in spite of significant modeling errors the MRAC idea is well realized and in the same time precise tracking can be achieved. Up to the information of the authors this is the first application of the RFPT-based approach in the synchronization of Chua circuits.