摘要
本研究中提出了一種新的動態結構，是在所謂的動態簡化分解模糊系統（dynamic simplified decomposed fuzzy systems, dynamic SDFS）中使用動態隸屬函數(dynamic membership functions)。動態SDFS被當作自適應模糊控制中的模糊近似器。我們所提出的動態結構是基於分解模糊系統（decomposed fuzzy systems, DFS）和SDFS，以使用較少的模糊規則具有更好的建模性能。眾所周知，如果系統使用冗餘模糊規則，則在學習過程中可能發生過擬合現象(overfitting phenomenon)。當在學習過程中系統遇到干擾時，發現DFS會具有過度擬合現象; 同時SDFS在這種情況下沒有明顯的過度擬合現象。在動態 SDFS的概念即是在分層模糊系統(component fuzzy systems)的選擇中有更好的匹配，而在我們所提出的結構方法是動態的隸屬函數而不是固定的前鑑部分(fixed antecedent-parts)，而在我們匹配的模糊集是從DFS中最常被使用到的模糊規則。為了預測系統的下一個狀態，動態隸屬函數的模糊集由平衡桿角度(系統)的前一狀態所決定組成。每次迭代都會在模糊區間的特定範圍內更新新的模糊集合併與原始的固定模糊集合相結合。動態隸屬函數的主要目的是保持有用的模糊規則並放棄冗餘的模糊規則。此外，提出動態SDFS以提高學習效率並減少總模糊規則以滿足許多應用中所需的可能的實時約束。


關鍵字: 自適應模糊控制，機器人控制，高效學習，模糊逼近器，隸屬函數

Abstract
In this study, a novel dynamic structure with the use of dynamic membership functions in the so-called dynamic simplified decomposed fuzzy systems (dynamic SDFS) is proposed. The dynamic SDFS is to act as a fuzzy approximator in adaptive fuzzy control. The proposed dynamic structure is based on the decomposed fuzzy system (DFS) and SDFS to have better modeling performance with less fuzzy rules used. It is well-known that overfitting phenomena may occur in the learning process if redundant fuzzy rules are used. DFS are discovered to have overfitting phenomena when disturbances are given in the middle of learning; meanwhile SDFS does not have significant overfitting phenomena in this situation. In order to have better match in the selection of component fuzzy systems, which is a basis for dynamic SDFS, the proposed method considers dynamic membership functions instead of fixed antecedent-parts. The selected fuzzy sets are the most hit from DFS. For the purpose of predicting the next state of the system, the fuzzy sets of the dynamic membership function are made up of the former state of the angle of the pole. Each iteration will update new sets of fuzzy sets combine with the original fixed fuzzy set in the specific range of fuzzy interval. The main purpose of the dynamic membership functions are to keep the useful fuzzy rules and abandon the redundant fuzzy rules. Moreover, dynamic SDFS is proposed to enhance the learning efficiency and reduce the total fuzzy rules to satisfy possible real-time constraints required in many applications.

Keywords: Adaptive robust fuzzy control, Efficient learning, Fuzzy approximator

Contents
摘要 i
Abstract ii
致謝 iii
Contents iv
List of Figures vi
List of Tables ix
Chapter 1 Introduction 1
1.1 Motivation 1
1.2 Literature Review 2
1.3 Organization of the Thesis 4
Chapter 2 Basic Concept 5
2.1 Fuzzy Control 5
2.2 Adaptive Control 6
2.3 Indirect Adaptive Fuzzy Robust Control 8
Chapter 3 Control System Structure Design 14
3.1 Decomposed Fuzzy Systems (DFS) 14
3.2 Simplified Decomposed Fuzzy Systems (SDFS) 19
3.3 Simulation Results and Comparisons of DFS and SDFS 21
3.3.1 Set Initial Condition and Control Objectives 21
3.3.2 Simulation and Comparison 25
3.3.3 Overfitting Phenomenon and Overfitting Test 30
3.4 Dynamic Structure 36
3.4.1 Dynamic Simplified Decomposed Fuzzy System 36
3.4.2 Dynamic Membership Function 38
Chapter 4 Simulation Results 44
4.1 Set Initial Condition and Control Objectives 44
4.2 Simulation of Dynamic Simplified Decomposed Fuzzy System 47
4.3 Simulation of Dynamic Membership Function 49
4.3.1 Dynamic Membership Function with DFS 49
4.3.2 Dynamic Membership Function with SDFS 54
4.3.3 Dynamic Membership Function with Dynamic SDFS 57
4.4 Comparison without Robust Control Scheme 60
4.5 Comparison with Robust Control Scheme 65
Chapter 5 Conclusions and Future Work 68
5.1 Conclusions 68
5.2 Future Work 69
References 70

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