臺灣博碩士論文加值系統

本論文致力於多項式模糊控制系統的研究並提出多種多項式模糊控制器的設計方法，包含穩定控制器設計、強健H∞控制器設計、智慧型控制器設計與智慧型強健H∞控制器設計。針對穩定控制器與強健H∞控制器，文中採用非二次Lyapunov函數分析系統的穩定性並提出基於SOS的穩定條件，透過SOSTOOLS等數值分析軟體求解這些穩定條件來獲得控制器增益。在穩定控制器設計的研究上，探討了如何改變系統的響應速度與設計限制輸出的控制器，並提出具衰退率指標的穩定條件與輸出限制。為了對抗外部干擾與模式不確定性，本文提出強健H∞控制器設計的方法。首先，針對連續時間與離散時間的非線性系統，文中提出可描述模式不確性與外部干擾的多項式模糊控制系統，並透過H∞準則與非二次Lyapunov函數分析系統的穩定性來推導強健H∞穩定條件。為了改善穩定控制器與強健H∞控制器的性能，文中採用量子進化演算法結合SOS穩定條件的方法，提出智慧型控制器設計與智慧型強健H∞控制器設計。在這個方法裡，量子進化演算法可在找尋控制增益的過程中，同時透過SOS穩定條件確保系統的穩定性，並篩選出滿足性能要求的最佳控制增益。此外，為了提高SOS穩定條件被滿足的機率，文中採用多項式Lyapunov函數分析系統的穩定性並推導出寬鬆的穩定條件與寬鬆的強健H∞穩定條件。論文裡將透過多個模擬實驗說明每個定理的可行性與有效性。

This dissertation investigates polynomial fuzzy control systems and proposes several polynomial fuzzy controllers, including stable controller design, robust H∞ controller design, intelligent controller design, and intelligent robust H∞ controller design. System stability is analyzed using a non-quadratic Lyapunov function, and stability conditions based on the sum-of-squares (SOS) are proposed. The control gains are obtained by solving these stability conditions using numerical analysis software such as SOSTOOLS. In the study of stable controller design, methods of changing the response speed of the system are discussed, and a controller is designed to limit the output and present the decay-rate-index-based stability conditions and output constraints. In order to ensure robustness to external disturbances and model uncertainties, this dissertation presents robust H∞ controller design methods. First, polynomial fuzzy control systems, which can describe model uncertainties and external disturbances, are proposed for continuous-time and discrete-time nonlinear systems. The robust H∞ conditions are derived using the H∞ criterion and non-quadratic Lyapunov function to analyze system stability. In order to improve the performance of the stable controller and the robust H∞ controller, a method combining the quantum-inspired evolutionary algorithm (QEA) and SOS-based stability conditions is presented, and an intelligent controller and intelligent robust H∞ controller design are presented. In this method, QEA adopts the SOS-based stability conditions to guarantee system stability during the control gains search procedure. Accordingly, the optimal control gain, which is satisfied with the performance requirements, will be screened out. In addition, to enhance the probability of complying with the SOS-based stability conditions, the polynomial Lyapunov function is used to analyze closed-loop system stability, and relaxed stability and relaxed robust H∞ stability conditions are derived. Several simulations demonstrate the effectiveness and feasibility of each proposed method.

摘要 I
Abstract II
Contents III
List of Figures VI
List of Tables IX
Acronyms X
List of Abbreviations XI
Chapter 1 Introduction 1
1.1 Background and Motivation 1
1.2 Main Contributions 5
1.3 Dissertation Outline 5
Chapter 2 Polynomial Fuzzy Control Systems 7
2.1 Polynomial Fuzzy Model 7
2.2 Polynomial Fuzzy Controller 10
2.3 SOS Decomposition and Stability Conditions 11
2.4 Application Example 13
2.5 Extended Designs 20
2.5.1 Stability Conditions with Decay Rate 20
2.5.2 Controller Design with Decay Rate 22
2.5.3 Output Constrains 25
2.5.4 Controller Design with Output Constrains 27
2.6 Summary 29
Chapter 3 Robust H∞ Control of Continuous-time Polynomial Fuzzy Systems .30
3.1 Continuous-time Polynomial Fuzzy Control System with Model Uncertainties and External Disturbances 30
3.2 Continuous-time Robust Polynomial Fuzzy Control 32
3.2.1 SOS-based Robust Stability Conditions 32
3.2.2 Numerical Example 3.1 35
3.2.3 Numerical Example 3.2 39
3.3 Continuous-time Robust H∞ Polynomial Fuzzy Control 40
3.3.1 SOS-based Robust H∞ Stability Conditions 41
3.3.2 Numerical Example 3.3 43
3.4 Summary 53
Chapter 4 Robust H∞ Control of Discrete-time Polynomial Fuzzy Systems 55
4.1 Discrete-time Polynomial Fuzzy Model 55
4.2 Discrete-time Polynomial Fuzzy Controller 57
4.3 Discrete-time Robust H∞ Polynomial Fuzzy Control 58
4.3.1 SOS-based Robust H∞ Stability Conditions 58
4.3.2 Numerical Example 4.1 60
4.4 Operation-domain-based Robust H∞ Controller Design 65
4.4.1 OD-based Robust H∞ Stability Conditions 65
4.4.2 Numerical Example 4.2 67
4.5 Summary 74
Chapter 5 SOS-based Polynomial Fuzzy Controller Design Using QEA 75
5.1 Quantum-inspired Evolutionary Algorithms 75
5.2 Polynomial-Lyapunov-function-based Stability Conditions 79
5.3 The Procedure of SOS-based QEA 80
5.4 Computer Simulations 80
5.4.1 Controller Design via SOS-based QEA 82
5.4.2 Performance Comparison with Different Approaches 90
5.4.3 Discussion on Different Order Polynomial Lyapunov Function 93
5.5 Summary 97
Chapter 6 Optimally Robust H∞ Controller Design of Polynomial Fuzzy Systems Using QEA 98
6.1 Optimally Robust H∞ Controller Design of CPFS Using QEA 98
6.1.1 SOS-based Optimally Robust H∞ Stability Conditions 99
6.1.2 Numerical Example 6.1 101
6.1.3 Relaxed SOS-based Optimally Robust H∞ Stability Conditions 107
6.1.4 Numerical Example 6.2 110
6.1.5 Numerical Example 6.3 114
6.2 Optimally Robust H∞ Controller Design of DPFS Using QEA 116
6.2.1 SOS-based Optimally Robust H∞ Stability Conditions 116
6.2.2 Numerical Example 6.4 120
6.2.3 Numerical Example 6.5 125
6.3 Summary 127
Chapter 7 Conclusions and Future Works 128
7.1 Conclusions 128
7.2 Future Works 128
References… 130
Appendix…. 138
Publication List 158

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