本研究的主旨是探討如何將類神經網路及模糊控制方法，以及高頻抖動訊號應用到混沌系統。在本研究中，我們首先建立混沌系統的類神經網路模型，並將其轉換成類似模糊形式的線性為分函式。但是不可避免地，模型與真實系統間存在著近似誤差的問題。此時強健模糊控制設計來克服類神經網路模型與混沌系統中誤差問題。然而如果我們所設計出的模糊控制器不能使系統穩定，則加入高頻抖動訊號來協助穩定系統。當高頻抖動訊號的頻率愈高，系統的輸出就會與其相對應之模型－類神經網路鬆弛系統的輸出愈接近，所以我們可以利用類神經網路鬆弛系統的穩定度，來探討加入高頻抖動訊號後混沌系統的穩定度來探討加入高頻抖動訊號後混沌系統的穩定度。最後，藉著找出適當的高頻抖動訊號波形、振幅及頻率，來有效控制混沌運動到一個期望的週期性軌跡或是一個穩定的狀態。

This thesis presents an effective approach for controlling chaos. First, a neural-network (NN) model is employed to approximate the chaotic system. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of NN model. Based on the LDI state-space representation, a robustness design of fuzzy control is proposed to overcome the effect of modeling error between chaotic systems and NN models. If the designed fuzzy controller cannot asymptotically stabilize the chaotic system, a high frequency signal, commonly called dithers, into the chaotic systems. According to the relaxed method, an appropriate dither is introduced to suppress chaotic motion. If the frequency of dither is high enough, the outputs described by the dithered chaotic system and the outputs of its corresponding mathematical model — the relaxed system would be made as close as desired. Thus, the closed-loop dithered chaotic system’s behavior can be rigorously predicted by establishing that of the closed-loop relaxed system. Finally, a numerical example with simulations is given to illustrate the concepts discussed throughout this thesis

摘要………………………………………………………………………i
Abstract………………………………………………………………ii
誌謝……………………………………………………………………………iv
Contents…………………………………………………………………………v
Contents of Figures…………… ………………………………………………vi
Chapter 1 Introduction………………………………………………………1
Chapter 2 Introduction to chaos………………………………………………4
Chapter 3 Neural-Network Based Approach and Fuzzy Control…………8
3.1. Neural-Network Model of Chaotic System………………………………8
3.2. Fuzzy Controller………………………………………………………11
Chapter 4 Robustness Control Design and Stability Analysis……………13
4.1. Modeling Error…………………………………………………………13
4.2. Stability Analysis………………………………………………………15
Chapter 5 Dithered System and Stability Analysis…………………………18
5.1. Dithered Chaotic System and Relaxed Model…………………………18
5.2. Closed-loop Relaxed System and Modeling Error……………………20
5.3. Stability Analysis………………………………………………………21
Chapter 6 Simulation Results………………………………………………25
Chapter 7 Brief Discussion and Conclusion…………………………………35
7.1 Discussion………………………………………………………………35
7.2 Conclusion……………………………………………………………….36
Bibliography…………………………………………………………………37

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