Hybrid Function Projective Synchronization of Chaotic Systems with Fully Unknown Parameters

Abstract

To compensate for projective synchronization (PS) and function projective synchronization (FPS), we propose a hybrid function projective synchronization (HFPS), which applies the different time-varying functions as the synchronization scaling factors. Based on the adaptive control method, we design a simple controller and a set of update laws of unknown parameters to carry out HFPS in identical and different chaotic systems with fully unknown parameters. According to the Lyapunov stability theorem and the Barbalat lemma, we prove the asymptotical stability of the error dynamical system at the origin. Then two numerical examples are given to validate the feasibility and effectiveness of the developed procedure in this paper. Key Words: Hybrid function projective synchronization; Lyapunov stability theorem; Adaptive control; Unknown parameters