在本論文中主要利用可變結構控制理論，探討對於具/不具時延混沌系統同步化之問題。基於主-僕概念、李亞普諾夫穩定性定理，對於Lorenz、 Chua’s電路、Rossler、Hopfield及網格型類神經系統，包含不確定性因子/非線性輸入/未知傳輸時間延遲/扇形非線性/時變延遲等問題，設計強健控制器，以保證系統達到同步。首先，對於具非匹配擾動之Lorenz系統設計強健可變結構控制器來保證系統可順利進入滑動模式，並討論非匹配擾動對系統控制性能的影響。第二部份，對於一類具有未知系統參數及輸入非線性混沌系統提出適應性強健同步控制器的設計方法。第三部份，考慮一類特定具時變及非線性輸入之類神經系統之同步化問題。最後，本文也提供一些說明的範例來證明所提出之主要結果。

In this dissertation, the synchronization problem of chaotic systems with/without time-delay via the variable structure control (VSC) approach is investigated. This includes the development of the mismatch uncertainties/input nonlinearity/unknown channel time-delay/sector nonlinearity/time-varying delays problems for a series of Lorenz systems, Chua’s circuit systems, Rossler systems, Hopfield neural networks (HNN), Cellular neural networks (CNN). Based on the drive-response concept and the Lyapunov stability theorem, some controllers are proposed which guarantee synchronization for a class of chaotic systems. Firstly, a VSC controller is presented to ensure the occurrence of the sliding mode for a class of Lorenz systems subject to mismatch uncertainties. Secondly, the adaptive synchronization of a class of chaotic systems with both unknown system parameters and the nonlinearity in the control input is addressed. Thirdly, the synchronization problem for a particular class of neural networks subject to time-varying delays and input nonlinearity is investigated. Some illustrative examples are included to demonstrate the effectiveness of the proposed synchronization schemes.

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