Adaptive synchronization of chaotic systems and its application to secure communications

This paper addresses the adaptive synchronization problem of the drive-driv en type chaotic systems via a scalar transmitted signal. Given certain stru ctural conditions of chaotic systems, an adaptive observer-based driven sys tem is constructed to synchronize the drive system whose dynamics are subje cted to the system's disturbances and/or some unknown parameters. By approp riately selecting the observer gains, the synchronization and stability of the overall systems can be guaranteed by the Lyapunov approach. Two well-kn own chaotic systems: Rossler-like and Chua's circuit are considered as illu strative examples to demonstrate the effectiveness of the proposed scheme. Moreover. as an application, the proposed scheme is then applied to a secur e communication system whose process consists of two phases: the adaptation phase in which the chaotic transmitter's disturbances are estimated; and t he communication phase in which the information signal is transmitted and t hen recovered on the basis of the estimated parameters. Simulation results verify the proposed scheme's success in the communication application. (C) 2000 Elsevier Science Ltd. All rights reserved.