Abstract
This paper addresses a unified mathematical expression describing a class of chaotic systems, for which the problem of synchronization and anti-synchronization between different chaotic systems with fully uncertain parameters and different structure are studied. Based on the Lyapunov stability theory, a novel, simple, and systemic adaptive synchronization controller is designated, the analytic expression of the controller and the adaptive laws of parameters are developed. Moreover, the proposed scheme can be extended to anti-synchronize a class of chaotic systems. Two chaotic systems with different structure and fully uncertain parameters are employed as the examples to show the effectiveness of the proposed adaptive synchronization and anti-synchronization schemes. Additionally, the robustness and noise immunity of the adaptive synchronization scheme is investigated by measuring the mean squared error of the systems.
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Li, XF., Leung, A.CS., Han, XP. et al. Complete (anti-)synchronization of chaotic systems with fully uncertain parameters by adaptive control. Nonlinear Dyn 63, 263–275 (2011). https://doi.org/10.1007/s11071-010-9802-7
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DOI: https://doi.org/10.1007/s11071-010-9802-7