區域型Takagi-Sugeno模糊系統之 H2/H∞ 區域控制器設計

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吳盛明(Sheng-Ming Wu) 查詢紙本館藏

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論文名稱

區域型Takagi-Sugeno模糊系統之 H2/H∞ 區域控制器設計
(H2/H∞ Regional Controller Design for Takagi-Sugeno Fuzzy Region Systems)

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摘要(中)

Takagi-Sugeno (T-S) 模糊控制器設計方法多採用平行分配補償 (Parallel Distributed Compensation - PDC) 之設計觀念並結合里阿伯諾 (Lyapunov) 穩定法則來做T-S模糊模型的設計及分析。求解 T-S模糊系統之輸出迴授增益值時是以矩陣型態呈現，控制器求解的過程一般都是轉換成線性矩陣不等式(Linear Matrix Inequalities - LMI) 來做處理，不過，當T-S 模糊系統所包含大量的模糊規則數，轉換後的LMI 總數目也急遽增加。在此情況下，LMI演算法之無解機率大幅提高，既使有解也需要高速的運算硬體執行解模糊化的計算。然而，模糊輸出迴授增益值比狀態迴授控制還要更複雜、更難設計的原因是這類問題無法轉換成LMI的形式來求解。故 (Non-LMI) NLMI的問題比LMI總數目遽增來的棘手許多。
瞭解前述一些問題的癥結所在，於是本論文利用模糊區域觀念 (Fuzzy Region Concept) 將原本的模糊子系統分割成數個模糊區域。由於一個模糊區域控制器必須使得數個模糊子系統穩定，於是在控制器的設計過程中引進強健控制的技巧。由上所述可知，本論文之目的就是設計相對應於每一個模糊區域的迴授增益值，然後使得整個T-S 模糊區域系統得以全區穩定，進而達到利用少量的模糊控制規則達到控制目的。本論文亦將模糊區域觀念處理非線性系統之非凸集合(non-convex)、NLMI問題，於條件下以求得輸出迴授控制器。於此，我們結合兩種演算法-基因演算法及LMI演算法，以達成模糊區域型-輸出迴授控制器之設計。本論文中，基因演算法扮演搜尋適合系統之輸出迴授增益值的角色，並加快基因演算法的速度。現在既然已經用基因演算法找出輸出迴授增益值了，非LMI的問題也就迎刃而解，而里阿伯諾穩定法則中的共同正定矩陣就可由LMI演算法輕易的求出。複合式演算法(GA/LMI)會相輔相成的調整最佳值，直到所有的穩定條件都滿足且符合需求。最後，本論文最主要的貢獻是 (i)當系統含有大量的模糊規則數時，利用模糊區域觀念減少控制規則數量。另一項優點為本方法可避免在PDC的設計中需考慮規則干擾的穩定性問題，(ii)所提出的複合式演算法(GA/LMI)成功的以簡單的想法、清楚的數學推導處理模糊區域靜態輸出迴授之穩定性問題。

摘要(英)

In recent years, the majority of Takagi-Sugeno (T-S) fuzzy controller designs were developed by using the concept of Parallel Distributed Compensation (PDC) and the Lyapunov stability criterion. The stability conditions were solved by Linear Matrix Inequality (LMI) solver. PDC-based fuzzy controller involves many controller rules of LMIs if the T-S fuzzy model contains lots of plant rules. Especially in the static output feedback fuzzy control design, the design becomes much more difficult and complex than state feedback one because it belongs to a Non-Linear Matrix Inequalities (NLMIs) problem.
This dissertation uses the fuzzy region concept to partition the original plant rules into several fuzzy regions. The purpose of this dissertation is to design controller rules for each fuzzy region such that the overall fuzzy model is stabilized. In light of the aforementioned concerns, this dissertation also deals with the non-convex issue in a nonlinear system which was presented by the T-S fuzzy region system with sense. It is expected to mix a GA with an LMI solver to achieve the design purpose. The GA is employed for seeking suitable feedback gains from a prescribed fitness function. Since the feedback gains are given,the Lyapunov stability inequalities of static output feedback syntheses can be dealt with the LMI solver. To carry on, GA will support LMI to tune the solutions until all stability conditions are satisfied. This hybrid algorithm tackles the static output feedback fuzzy control problems with a simple idea and clear mathematical derivations. Finally, we emphasize that the main contributions of this dissertation are (i) the proposed region concept can greatly reduce the total number of LMIs and controller rules (ii) a simple and flexible method to solve this NLMI problem and find a regional static output feedback gain is proposed.

關鍵字(中)

★ Takagi-Sugeno 模糊系統
★ 模糊區域觀念
★ 線性矩陣不等式
★ Lyapunov 穩定準則

關鍵字(英)

★ Takagi-Sugeno fuzzy systems
★ fuzzy region concept
★ Linear Matrix Inequality (LMI) and Lyapunov stab

論文目次

Table of Contents
Abstract III
Nomenclature V
Acronyms VI
List of Tables VII
List of Figures VIII
Chapter 1 INTRODUCTION 1
1.1 Historical Background 1
1.2 Literature Reviews 3
1.3 Motivations and Purposes 6
1.4 Contributions 9
1.5 Organization 10
Chapter 2 PRELIMINARIES AND PROBLEM FORMULATIONS 11
2.1 Introduction 11
2.2 Typical T-S Fuzzy System and Its Stability Conditions 12
2.2.1 Descriptions of Typical T-S Fuzzy Models 12
2.2.2 PDC-based State Feedback Fuzzy Controller Design 14
2.3 Regional-based T-S Fuzzy System and Its Stability Conditions 17
2.3.1 Descriptions of Regional-based T-S Fuzzy Models 17
2.3.2 Regional-based State Feedback Fuzzy Controller Design 20
2.4 Summary 24
Chapter 3 REGION-BASED STATE FEEDBACK FUZZY CONTROL WITH MULTIPLE PERFORMANCE CONSTRAINTS 25
3.1 Introduction 25
3.2 Preliminaries and Problem Descriptions 26
3.3 Main Results 30
3.3.1 Regional-based State Feedback Fuzzy Controller Design 31
3.3.2 Stability Analysis for Regional-based State Feedback Fuzzy Control with Performance Constraints 36
3.4 A Numerical Example 41
3.5 Summary 52
Chapter 4 REGION-BASED STATIC OUTPUT FEEDBACK FUZZY CONTROL 53
4.1 Introduction 53
4.2 Preliminaries and Problem Descriptions 54
4.3 Main Results 57
4.3.1 Regional-based Static Output Feedback Fuzzy Controller Design 57
4.3.2 Synthesis of Regional-based Static Output Feedback Fuzzy Control via LMI/GA algorithms 60
4.4 A Numerical Example 64
4.5 Summary 71
Chapter 5 REGION-BASED STATIC OUTPUT FEEDBACK FUZZY CONTROL WITH MULTIPLE PERFORMANCE CONSTRAINTS 72
5.1 Introduction 72
5.2 Problem Descriptions 73
5.3 Main Results 75
5.3.1 Stability Analysis for Regional-based Static Output Feedback Fuzzy Control with Performance Constraints 75
5.3.2 Regional-based Static Output Feedback Fuzzy Controller Design 82
5.4 A Numerical Example 89
5.5 Summary 96
Chapter 6 CONCLUSIONS AND RECOMMENDATIONS 97
References 99
Publication List 104

參考文獻

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指導教授

鍾鴻源(Hung-Yuan Chung)

審核日期

2008-7-9

推文