臺灣博碩士論文加值系統

在過去文獻中所探討的協方差控制問題多針對線性系統。因此，在本篇論文中，我們將嘗試推廣此方法至內含狀態觀測之非線性隨機系統上。本論文是討論被建模在Takagi-Sugeno (T-S) 模糊模型上的閉迴路連續時間及離散時間觀測器基礎型回授非線性隨機系統，因為動態的T-S模型特性與非線性系統特性相似，所以我們使用T-S模型來表示非線性系統。根據平行分布補償的方法，可使用線性的回授增益值來驅動非線性隨機系統。
在本論文中，我們嘗試結合協方差控制理論及T-S模糊模型的特點來處理閉迴路連續時間及離散時間觀測器基礎型非線性隨機系統的控制問題。在我們所提出方法的前半部中，我們指定一個共同狀態協方差矩陣去取代T-S模糊模型下穩定條件中所需的共同正定矩陣。受制於這個特別的共同正定狀態協方差矩陣，線性的狀態或輸出回授控制增益將直接地由廣義逆矩陣定理求出。在本論文後半部中，我們將獲得一個在連續時間一個在離散時間T-S模糊模型下去求解線性回授增益的方法，同時使得方法達到系統的特性條件。並且，在此所提出的模糊控制問題可以被簡化為線性矩陣不等式的問題。此外，我們舉一些範例來證明我們所提供方法的有效性。

A complete approach, which is called covariance control theory, for assigning the entire state covariance matrix to the closed-loop systems via state feedback or output feedback controllers has been developed in past years. However, the systems considered in these literatures are often linear ones. Hence, we will attempt to extend the covariance control theory to nonlinear stochastic systems in this thesis. This thesis discusses a class of continuous-time and discrete-time observer-based nonlinear stochastic systems, which are modeled by the Takagi-Sugeno (T-S) fuzzy models. Because of the dynamic properties of T-S fuzzy model and nonlinear system are similar; hence, we can represent the nonlinear systems by T-S fuzzy models. According to Parallel Distributed Compensation (PDC) concept, the nonlinear stochastic systems can be driven by the linear feedback gains. In other words, a linear feedback controller can be designed for each local linear model by linear feedback control techniques. The closed-loop fuzzy controller consists of these linear controllers.
In this thesis, we attempt to combine the characteristics of covariance control theory and T-S fuzzy models to deal with the control design problems of the closed-loop continuous-time and discrete-time observer-based nonlinear stochastic systems. The first half part in the present approach is to assign a common state covariance matrix instead of the common positive definite matrix for the stability conditions of closed-loop continuous-time and discrete-time observer-based T-S fuzzy stochastic control systems. In subject to this common positive definite state covariance matrix, the linear observer-based fuzzy control gains will then be directly solved by the theory of generalized inverse. In the latter half part of this thesis, we derive a practical fuzzy control method to solve the linear observer-based fuzzy control feedback gains for the continuous-time and discrete-time observer-based T-S type fuzzy controllers, which can achieve multiple system performance constraints simultaneously. Moreover, the presented fuzzy control design problem can be reduced to a Linear Matrix Inequalities (LMI) problem. Besides, some numerical examples are provided to verify the effects of the proposed method.

TABLE OF CONTENTS

Page
ABSTRACT i
NOMENCLATURE iii
ACRONYMS iv
LIST OF FUGURES v
TABLE OF CONTENTS viii

CHAPTER 1 Introduction 1
1.1 Background and Motivation 1
1.2 Review of Previous Works 4
1.3 Purpose and Contributions 6
1.4 Organization of this Dissertation 8

CHAPTER 2 Covariance Control for
Continuous-time Observer-based
T-S Fuzzy Models 9
2.1 Introduction 9

Page
2.2 Properties of the Continuous-time Observer-based
Nonlinear Stochastic Systems Using T-S Fuzzy Models 10
2.3 Continuous-time Observer-based T-S Fuzzy
Controller Design 19
2.4 Numerical Examples 23
2.5 Summary 36

CHAPTER 3 Covariance Control for
Discrete-time Observer-based
T-S Fuzzy Models 37
3.1 Introduction 37
3.2 Descriptions of the Discrete-time Observer-based
Nonlinear Systems Using T-S Fuzzy Models 38
3.3 The Solutions of Discrete-time Observer-based Gains for T-S Type Fuzzy Controllers 46
3.4 Numerical Examples 53
3.5 Summary 64

CHAPTER 4 Multiple Constrained Fuzzy Control
for Continuous-time Observer-based
T-S Fuzzy Models via LMI Methods 65
Page
4.1 Introduction 65
4.2 Stability Conditions for Continuous-time
Observer-based Nonlinear Stochastic Systems Using
T-S Fuzzy Models 66
4.3 Continuous-time Observer-based T-S Type Fuzzy
Controller Design with Multiple Performance
Constraints 70
4.4 Numerical Examples 74
4.5 Summary 87

CHAPTER 5 Multiple Constrained Fuzzy Control
for Discrete-time Observer-based
T-S Fuzzy　Models via LMI Methods 88
5.1 Introduction 88
5.2 Stability Conditions for Discrete-time Observer-based
Nonlinear Stochastic Systems Using T-S Fuzzy
Models 89
5.3 Solutions for the Multiple Constrained Fuzzy Control
Problems of Discrete-time Observer-based T-S Type
Fuzzy Controller 93
5.4 Numerical Examples 95
5.5 Summary 100
Page
CHAPTER 6 Conclusions and Recommendations 102
6.1 Work in Retrospect 102
6.2 Avenues for Future Research 103

APPENDIX 105
REFERENCES 106
PUBLICATION LIST 111

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