Adaptive feedback controller for projective synchronization. (English) Zbl 1144.93364

Hu, Manfeng; Xu, Zhenyuan

Nonlinear Anal., Real World Appl. 9, No. 3, 1253-1260 (2008).

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:

93D21	Adaptive or robust stabilization
37N35	Dynamical systems in control
93C40	Adaptive control/observation systems
94A62	Authentication, digital signatures and secret sharing
93C15	Control/observation systems governed by ordinary differential equations

Keywords:

projective synchronization; adaptive control; secure communication

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