臺灣博碩士論文加值系統

本論文探討運用適應性控制對於統合型混沌系統之混沌行為抑制與蔡氏混沌系統之投影同步問題。所討論的統合型混沌系統及蔡氏混沌系統均考慮未知截止區之非線性輸入。本論文可以分成以下三大部分:
第一部分探討主-僕蔡氏混沌系統在受到截止區非線性輸入之混沌同步問題。並藉由滑動模式控制技術，建立了一個適應性可變結構控制法則來確保系統本身受到非線性截止區影響之下達成投影同步。
第二部分探討統合混沌系統受到系統不確定性和未知截止區非線性輸入控制之混沌抑制問題。並利用可變結構控制技術，建立一強健適應性控制法則於統合型混沌系統之混沌抑制。特別的是，本論文提出ㄧ新轉換面來簡化任務並確保閉迴路系統於滑動模式中之穩定性。
第三部分探討了尺度耦合信號於主-僕混沌系統同步問題。透過使用從主混沌系統之尺度耦合傳輸信號，設計出具有截止區非線性輸入之基於觀測器僕混沌系統。而輸出反饋控制方法則是用來實現主-僕系統廣義投影同步。此外，建立一個適應性觀測器控制法則，對於在未知的系統非線性以及截止區非線性參數影響下，確保廣義投影同步的達成。
每部分的理論均有嚴謹的理論定理及證明，並透過數值例子及電腦模擬以印證所提出的混沌系統控制與同步理論之正確性。

This dissertation investigates the chaos suppression problem of a class of unified chaotic systems and the projective synchronization problem of drive-response Chua’s chaotic systems using the adaptive control schemes with variable structure control and observer-based techniques. All considered unified chaotic systems and drive-response Chua’s chaotic systems are subjected to dead-zone nonlinear in input. This dissertation can be divided into the following three parts:
Firstly, the chaos synchronization problem of drive-response Chua’s systems with dead-zone nonlinear input is investigated. By using the sliding mode control technique, an adaptive control law is established which guarantees projective synchronization even when the dead-zone nonlinearity in the input is present.
Secondly, the chaos suppression problem of a class of unified chaotic systems subject to the system’s uncertainties and dead-zone nonlinearity in control input is investigated. A robust adaptive control law by employing the variable structure control technique is established to suppress chaos for a class of unified chaotic systems. In particular, a switching surface is newly proposed to simplify the task of ensuring the stability of the closed-loop system in the sliding mode.
Thirdly, the synchronization problem of drive-response chaotic systems with a scalar coupling signal is studied. By using the scalar transmitted signal from the drive chaotic system, an observer-based response chaotic system with dead-zone nonlinear in the input is designed. An output feedback control technique is derived to achieve the generalized projective synchronization between the drive system and the response system. Furthermore, an adaptive control law is derived that the generalized projective synchronization without the knowledge of system nonlinearity, and/or system parameters as well as that of parameters in dead-zone nonlinearity in input is ensured.
All theoretical developments in the dissertation are stated in Theorems and rigorously proved. Furthermore, several illustrative examples are given to demonstrate the effectiveness of the proposed control and synchronization schemes.

Abstract ..................................................I
摘要 ....................................................III
Acknowledgements .........................................IV
Contents ..................................................V
List of Figures .........................................VII
Nomenclature .............................................IX
CHAPTER 1 INTRODUCTION ....................................1
1.1 Motivation ............................................1
1.2 Key contributions .....................................3
1.2.1 Projective synchronization of chaotic systems with dead-zone in the control input ............................4
1.2.2 Adaptive variable structure control with input nonlinearity for chaotic systems ..........................4
1.2.3 Observer-based approach in generalized projective sunchronization of chaotic systems with unknown dead-zone input .....................................................4
1.3 Organization of this dissertation .....................5
CHAPTER 2 PROJECTIVE SYNCHRONIZATION OF CHUA`S CHAOTIC SYSTEMS WITH DEAD-ZONE IN THE CONTROL INPUT ...............7
2.1 Introduction ..........................................7
2.2. Synchronization problem of Chua’s system with dead-zone coupling .............................................7
2.3. Switching surface design for chaos synchronization ..10
2.4. Adaptive sliding mode controller design .............12
2.5. An illustrative example .............................15
2.6. Summary .............................................20
CHAPTER 3 ADAPTIVE VARIABLE STRUCTURE CONTROL FOR CHAOS SUPPRESSION OF A CLASS OF UNIFIED CHAOTIC SYSTEMS ........21
3.1 Introduction .........................................21
3.2. System formulation ..................................21
3.3. Switching surface design ............................24
3.4. AVSC design .........................................25
3.5. Simulation results ..................................31
3.6. Summary .............................................38
CHAPTER 4 GENERALIZED PROJECTIVE SYNCHRONIZATION OF CHAOTIC SYSTEMS WITH UNKNOW DEAD-ZONE INPUT: OBSERVER-BASED APPROACH .................................................39
4.1 Introduction .........................................39
4.2 Problem formulation ..................................39
4.3 Observer-based chaos synchronization schemes .........41
4.4 Illustrative examples ................................47
4.5 Summary ..............................................57
CHAPTER 5 CONCLUSIONS AND FUTURE WORKS ...................58
5.1 Conclusions ..........................................58
5.2 Future works .........................................59
References ...............................................60

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