臺灣博碩士論文加值系統

在本論文中討論由一些具有交互連結項的Takagi-Sugeno模糊模式子系統所組成的模糊隨機不確定大型系統的穩定化問題。吾人經由Takagi-Sugeno 模糊模型來描繪一個非線性系統，而Takagi-Sugeno 模糊模型是結合模糊集合和模糊推論能夠有效的來表示複雜的非線性系統。本論文有效的控制方法是基於李亞普諾夫穩定定理及穩定狀態協方差控制理論的基礎上，因此，進而提出兩個對於隨機不確定大型系統有效的強健控制方法。本論文首先利用可變結構控制理論的強健特性，提出一個模糊滑動模式控制器，其滑動面的選取是以積分形式來表示，而這個積分形式滑動面是設計使得參考模型輸入及系統誤差項消失在滑動模式中。另外，在給予一個指定的共通正定協方差矩陣，一個模糊狀態回授控制器可以經由相符合的回授增益值去確保T-S模糊隨機不確定大型系統的強健穩定度。最後，由數據的例子來驗證本論文所提出之控制器法則的有效性。

This thesis deals with the stabilization problem for the fuzzy stochastic uncertain large-scale system in which the system is composed of a number of Takagi-Sugeno fuzzy model subsystems with interconnections. We represent a nonlinear plant with a Takagi-Sugeno fuzzy model that provides an effective method to represent complex nonlinear systems by fuzzy sets and fuzzy reasoning. Based on the Lyapunov stability theorem and the theory of the steady state covariance control, two feasible and effective approaches to the robust control problem of the stochastic uncertain large-scale systems are developed in this thesis. First, according to the robustness property of variable structure control, a fuzzy sliding mode controller with an integral function is designed such that the reference model input and the plant error term disappear on the sliding mode. Next, by assigning a common positive definite covariance matrix, the fuzzy state feedback controller can be developed by solving the corresponding state feedback gains such that the robust stability of the T-S fuzzy stochastic uncertain large-scale systems can be guaranteed. Finally, a numerical example is given to demonstrate the validity of the proposed two controllers in this thesis.

CHINESE ABSTRACT i
ENGLISH ABSTRACT ii
ACKNOWLEDGEMENTS iii
TABLE OF CONTENTS iv
LIST OF FIGURES v
CHAPTER
1 INTRODUCTION 1
2 PROBLEM FORMULATION AND CONTROLLER DESIGN 4
2.1 T-S Fuzzy Systems and Preliminaries 4
2.2 Fuzzy Sliding Mode Controller Design for Stochastic Uncertain
Large-Scale Systems 6
2.2.1 Choice of Control Function 10
2.2.2 Design of Control Feedback Gain Matrix 15
2.3 State Feedback Controller Design for Stochastic Uncertain Large-
Scale Systems 18
2.3.1 Design of T-S Type Fuzzy Controller 18
3 EXAMPLES AND SIMULATION RESULTS 23
3.1 Fuzzy Sliding Mode Control Approach 23
3.2 State Feedback Control Approach 33
4 CONCLUSION 41
REFERENCES 42

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