臺灣博碩士論文加值系統

現今的生活裡，在真實系統中時常存在著許許多多的隨機行為，因此對於隨機系統之穩定性分析與控制器設計變得越來越重要。在這篇論文中，我們藉由協方差控制理論、極點配置理論和強健控制理論，對含有隨機行為之擾動非線性系統提出了一個強健模糊控制器的設計方法。首先，以擾動Takagi-Sugeno模糊模型來表示我們的目標非線性系統，並利用平行分布補償方法來做模糊控制器的設計。接下來，考慮到擾動Takagi-Sugeno模型的穩定性分析與系統性能，我們發展出受限於多重性能條件，包含狀態方差限制、輸出方差限制、極點配置限制之李亞普諾夫(Lyapunov)穩定性條件。本論文提出的滿足多重性能限制之擾動模糊控制器設計問題可以被有效地轉化為線性矩陣不等式問題，並可利用凸優化程式演算法解決此問題。最後，一些實際的非線性系統被選擇來驗證本論文之強健模糊控制器設計方法的適用性及有效性。

Nowadays, the stability analysis and controller design of stochastic systems have become much more important since the stochastic behaviors are usually exist in practical systems. Because of the reason, a robust fuzzy controller design approach is proposed by covariance control theory, pole placement theory and robust control theory in this thesis. At first, nonlinear systems are expressed as a perturbed Takagi-Sugeno fuzzy model and the so-called parallel distributed compensation method is applied for the fuzzy controller design. Next, considering the stability analysis and the performance of the perturbed Takagi-Sugeno fuzzy model, corresponding Lyapunov stability conditions subject to multiple performance constraints, including state variance constraint, output variance constraint and pole placement constraint are developed. Then, the proposed fuzzy control problem can be effectively transferred into the linear matrix inequality problem and it can be solved by the convex optimal programming algorithm. At last, several nonlinear practical systems are selected to verify the applicability and effectivity of the proposed robust fuzzy controller design method.

摘要 I
Abstract II
Index of Chapters and Sections III
List of Figures V
Nomenclature VIII
Acronyms IX

Chapter 1 Introduction

1.1 Background and Motivation 2
1.2 Review of Previous Work 4
1.3 Purposes and Contributions 5
1.4 Thesis Organization 6

Chapter 2 Robust Fuzzy Controller Design for
Continuous-Time Perturbed Stochastic
Nonlinear Systems Subject to Multiple
Performance Constraints

2.1 System Descriptions and Problem Statements 8
2.2 Robust Fuzzy Controller Design with State Variance
Constraint and Output Variance Constraint 13
2.3 Pole Placement Constrained Robust Fuzzy Controller
Design Subject to State Variance Constraint and
Output Variance Constraint 18
2.4 Summary 21

Chapter 3 Robust Fuzzy Controller Design for Discrete-
Time Perturbed Stochastic Nonlinear Systems
Subject to Multiple Performance Constraints

3.1 System Descriptions and Problem Statements 23
3.2 Robust Fuzzy Controller Design with State Variance
Constraint and Output Variance Constraint 28
3.3 Pole Placement Constrained Robust Fuzzy Controller
Design Subject to State Variance Constraint and
Output Variance Constraint 33
3.4 Summary 35

Chapter 4 Simulations of Multiple Performance
Constrained Robust Fuzzy Control for
Practical Perturbed Stochastic Nonlinear
Systems

4.1 Simulation of Practical Nonlinear Systems Subject
to Multiple Performance Constraints with
Adjustment for Pole Placement Constraint
4.1.1 Simulation of Continuous-Time TORA System 37
4.1.2 Simulation of Discrete-Time Nomoto’s Ship
Steering System 48
4.2 Simulation of Practical Nonlinear Systems Subject
to Multiple Performance Constraints Compared with
Other Controller Design Method
4.2.1 Simulation of Continuous-Time Fossen’s Ship
Steering System 57
4.2.2 Simulation of Discrete-Time Truck-Trailer System
83

Chapter 5 Conclusions

5.1 Conclusions 102
5.2 Future Works 103

Reference 104
Publication 109

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