本論文中利用適應順滑模態追蹤控制器成功地使得兩個具有匹配與非匹配擾動的相同混沌系統得以達到混沌同步。基於李亞普諾夫穩定性理論與線性矩陣不等式最佳化技術本論文設計出順滑面方程式，以及在所提出的控制法則中引入了適應性調控機制，因此所設計的控制器可在系統進入順滑模態之後不僅能有效壓制非匹配擾動對受控系統之影響，也可使同步誤差控制在一個很小的範圍之內，且系統的擾動上界值不需事先知道，進而保證整個同步系統的穩定度。另外，論文中所提出來的同步技術可應用在安全通訊領域上。最後，分別以數值實例模擬來驗證控制器的可行性。

Synchronization of two identical chaotic systems with matched and mismatched perturbations by utilizing adaptive sliding mode control (ASMC) technique is presented in this thesis. The sliding surface function is designed based on Lyapunov stability theorem and linear matrix inequality (LMI) optimization technique. Adaptive mechanisms embedded in the proposed control scheme are used to adapt the unknown upper bounds of the perturbations. The designed tracking controller can not only suppress the mismatched perturbations when the controlled dynamics (master-slave) are in the sliding mode, but also drive the trajectories of synchronization errors into a small bounded region whose size can be adjusted through the designed parameters. The stability of overall controlled synchronization systems is guaranteed. Application of proposed chaotic synchronization technique to secure communication as well as several numerical examples are given to demonstrate the feasibility of the proposed design technique.

Contents
Abstract i
List of Figures iv
Chapter 1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Application to chaotic synchronization and secure communications . . . . . . . . 3
1.3 Brief Sketch of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Chapter 2 Design of Robust Sliding Mode Tracking Controllers 6
2.1 System Descriptions and Problem Formulations . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Design of Sliding Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Design of the Gain Matrix in the Sliding Function and Stability Analysis . . . . 11
2.4 Design of Adaptive Sliding Mode Tracking Controllers . . . . . . . . . . . . . . . . . . 19
Chapter 3 Application to Chaotic Synchronization and Secure Communications 25
3.1 Design of Adaptive Sliding Mode Tracking Controllers . . . . . . . . . . . . . . . . . . 26
Chapter 4 Numerical Examples and Simulations 32
4.1 Chaotic synchronization with mismatched perturbations . . . . . . . . . . . . . . . . . 32
4.2 Chaotic synchronization with matched perturbations . . . . . . . . . . . . . . . . . . . . 35
4.3 Chaotic secure communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Chapter 5 Conclusions and Future Works 51
Bibliography 52

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