Adaptive synchronization of identical chaotic and hyper-chaotic systems with uncertain parameters |
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Authors: | Xian-Feng Li Andrew Chi-Sing Leung Xiao-Jun Liu Xiu-Ping Han Yan-Dong Chu |
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Institution: | 1. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China;2. Department of Electronic Engineering, City University of Hong Kong, Hong Kong;3. School of Mathematics and Statistics, Tianshui Normal College, Tianshui 741001, China;4. School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, China |
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Abstract: | This paper addresses a unified mathematical expression describing a class of chaotic systems, for which the problem of adaptive synchronization between two nearly identical chaotic and hyper-chaotic systems with uncertain parameters is studied. Based on Lyapunov stability theory, a novel adaptive synchronization controller is designed, and the analytic expression of the controller and the adaptive laws of parameters are developed. The controller is simple and systemic, no parameters of the slave system are included in the controller, and, for some specific error systems, the controller can be simplified ulteriorly. New chaotic and a new hyper-chaotic systems with uncertain parameters are taken as the examples to show the effectiveness of the proposed adaptive synchronization method. |
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