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Adaptive synchronization of chaotic systems and its application to secure communications. (English) Zbl 0967.93059

The aim of this paper is to derive an adaptive observer-based driven system via a scalar transmitted signal which can attain not only chaos synchronization but can also be applied to secure communication of chaotic systems in the presence of the system’s disturbances and unknown parameters. Section 2 presents the class of chaotic systems considered and formulates the problem. Section 3 develops an adaptive observer-based driven system to synchronize the driving system with disturbances and unknown parameters. By appropriately selecting the observer gain vector such that the strictly positive real condition is satisfied, the synchronization and stability of the overall system are guaranteed by the Lyapunov stability theory with certain structural conditions. In Section 4, two well-known chaotic systems, Rösler-like and Chua’s circuit, are considered as illustrative examples to demonstrate the effectiveness of the proposed scheme. Moreover, in Section 5, the considered scheme is applied to a secure communication system whose process consists of two phases: the adaptive phase in which the chaotic transmitter’s disturbances are estimated, and the communication phase in which the information signal is transmitted and then recovered on the basis of the estimated parameters. Promising simulation results illustrate the proposed scheme in the communication application.

MSC:

93C40 Adaptive control/observation systems
93D21 Adaptive or robust stabilization
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
94A05 Communication theory
93C10 Nonlinear systems in control theory
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