
系統識別號 
U00263101201315163000 
論文名稱(中文) 
一類混沌系統有限時間同步之研究 
論文名稱(英文) 
Study on Finitetime Synchronization of a class of
Chaotic Systems 
校院名稱 
成功大學 
系所名稱(中) 
工程科學系碩博士班 
系所名稱(英) 
Department of Engineering Science 
學年度 
101 
學期 
1 
出版年 
102 
研究生(中文) 
萬兆麟 
研究生(英文) 
ZhangLin Wan 
學號 
N98961064 
學位類別 
博士 
語文別 
英文 
論文頁數 
64頁 
口試委員 
指導教授廖德祿 口試委員顏錦柱 口試委員連長華 口試委員姚賀騰 口試委員林瑞昇

中文關鍵字 
混沌系統
有限時間同步
伊藤公式
李亞普諾夫穩定性理論
適應性控制器
時間切換機制
滑動控制器

英文關鍵字 
chaotic systems
finitetime synchronization
Ito formula
Lyapunov stability theory
adaptive control
timedriven switching law
slidingmode control

學科別分類 

中文摘要 
本論文針對一類混沌系統作探討，利用伊藤公式和李亞普夫穩定性理論進行有限時間同步問題之研究。首先，針對利用高木菅野(TakagiSugeno, TS)模糊定理建構而成的具時間延遲混沌系統探討其穩定性，利用平行分散補償概念與李亞普諾夫穩定性理論，在其加入所設計的適應性控制器和適合的參數適應性更新機制，進行漸近同步與參數識別之研究。緊接著，對於具時間切換機制的隨機蔡氏電路進行部份有限時間同步相關之研究。其次，利用適當的切換面與滑動控制器之設計，確保其主僕時間切換隨機蔡氏電路的混沌同步和其誤差狀態的期望值為部份有限時間穩定。再者，在上述的研究基礎上，針對伴隨著時間切換機制的隨機羅斯勒混沌系統進行完整的有限時間同步之研究。在主要反饋控制器加入情況下，主僕時間切換隨機羅斯勒混沌系統能達到有限時間同步而其誤差狀態的期望值也能達到有限時間穩定。最後，利用電腦模擬結果驗證於本論文中所提之定理的有效性與正確性。

英文摘要 
In this dissertation, the problems of finitetime synchronization of a class of chaotic systems are investigated by using the Ito formula and Lyapunov stability theory. Firstly, the adaptive synchronization problem of general timedelayed chaotic systems which is represented by TakagiSugeno (TS) fuzzy model is considered. Based on parallel distributed compensation (PDC) scheme and Lyapunov stability theorem, an adaptive controller and corresponding parameters update laws are proposed to asymptotically synchronize the masterslave chaotic systems and achieve the parameters identification. Secondly, the partial finitetime synchronization between switched stochastic Chua’s circuits accompanied by a timedriven switching law is considered. By selecting an appropriate switching surface, the purposed slidingmode controller (SMC) is developed to guarantee the synchronization of switched stochastic masterslave Chua’s circuits and obtain the partial finitetime stability for the mean of error states. Finally, based on the above study, the full finitetime synchronization between switched stochastic Rössler chaotic systems accompanied by a timedriven switching law is presented. The finitetime synchronization of switched stochastic masterslave Rössler chaotic systems and the finitetime stability for the mean of error states are investigated with the proposed feedback controller. Some illustrative examples are given to demonstrate the effectiveness and correctness of the purposed theorems.

論文目次 
中文摘要...................................................I
Abstract.................................................II
Acknowledgements........................................III
Table of Contents........................................IV
List of Figures..........................................VI
Nomenclature...........................................VIII
Chapter 1 Introduction....................................1
1.1 Motivation....................................1
1.2 Brief Sketch of the Contents..................4
Chapter 2 Mathematical Preliminaries......................8
Chapter 3 Adaptive synchronization of chaotic systems
via T–S fuzzy model..............................13
3.1. Formulation of Main Chaotic System .........13
3.2. Adaptive Controller and Update Laws Design..15
3.3. Numerical Simulation Results................18
Chapter 4 Partial Finitetime Synchronization of Switched
Stochastic Chua's Circuits.......................25
4.1. Formulation of Switched Stochastic Chua's
Circuits.........................................25
4.2. SlidingMode Controller Design..............28
4.3. Numerical Simulation Results................34
Chapter 5 Finitetime Synchronization of Switched
Stochastic Chaotic system........................39
5.1. Formulation of Switched Stochastic Rössler
Chaotic System...................................39
5.2. Finitetime Controller Design...............41
5.3 Numerical Simulation Results.................44
Chapter 6 Conclusions and Future Works...................49
6.1 Conclusion...................................49
6.2 Future Works.................................50
References...............................................52

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