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Zbl 1144.93364
Hu, Manfeng; Xu, Zhenyuan
Adaptive feedback controller for projective synchronization. (English)
[J] Nonlinear Anal., Real World Appl. 9, No. 3, 1253-1260 (2008). ISSN 1468-1218

Summary: Due to the unpredictability of the scaling factor of projective synchronization in coupled partially linear systems, it is hard to know for sure the terminal state of the synchronized dynamics. In this paper, a simple adaptive linear feedback control method is proposed for controlling the scaling factor onto a desired value, based on the invariance principle of differential equations. Firstly, we prove the synchronizability of the proposed simple adaptive projective synchronization control method from the viewpoint of mathematics. Then, two numerical examples are presented to illustrate the applications of the derived results. Finally, we propose a communication scheme based on the adaptive projective synchronization of the Lorenz chaotic system. Numerical simulation shows its feasibility.

MSC 2000:: *93D21 Adaptive and robust stabilization
37N35 Dynamical systems in control
93C40 Adaptive control systems
94A62 Authentication and secret sharing
93C15 Control systems governed by ODE

Keywords: projective synchronization; adaptive control; secure communication

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