模糊動態系統之分段區域控制

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姓名

陳仕倫(Shih-lun Chen) 查詢紙本館藏

畢業系所

電機工程學系

論文名稱

模糊動態系統之分段區域控制
(Fuzzy Dynamic Systems Control via Piecewise Region-based Approach)

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摘要(中)

本篇論文在Takagi-Sugeno (T-S) 模糊系統下探討穩定分析與控制器設計，結合模糊區域概念和分段式Lyapunov穩定準則來設計模糊控制器，稱之為分段T-S模糊區域控制器。我們利用模糊區域概念將原來的子系統切割成數個模糊區域，當輸入的瞬間只會有一個模糊區域被觸發。一般利用T-S模糊區域概念所設計之控制器，必須要求出共同的正定矩陣以滿足系統穩定準則。但是，若一非線性系統是由許多的模糊規則數所組成，則共同可能會難求出。於此，本篇論文利用分段Lyapunov穩定準則只需求出各區域裡的個別正定矩陣，如此降低了判定方法的保守性，分段Lyapunov穩定準則以線性不等式(LMIs)表示，並藉此演算法算出個別區域的Lyapunov 矩陣及區域控制器。
因為分段T-S模糊區域概念有著簡化設計降低保守性及容易實現的優點，所以延伸分段Lyapunov穩定準則與模糊區域概念在不確定系統及觀察器的設計上，目的就是處理模糊區域的強健控制問題及設計對應於每一個模糊區域的觀察增益值，使得整個T-S模糊區域系統得以漸近穩定。再者，我們將利用數個數值例子來說明本論文理論的有效性。

摘要(英)

The stability analysis and controller design for T-S fuzzy system are discussed in this thesis. This thesis combines the fuzzy region concept and the piecewise Lyapunov stability criterion to design a new fuzzy controller which is called piecewise T-S fuzzy region controller. We utilized the fuzzy region concept to partition the original plant rules into several fuzzy regions. Only one partial fuzzy region is fired at the instant of each input vector being coming. The original controller design of T-S fuzzy region concept is required to find the common Lyapunov matrix. This common positive definite matrix may not exist when the T-S fuzzy system includes many fuzzy rules. Now we utilize the piecewise Lyapunov stability criterion and the regional concept to find the individual Lyapunov matrix and fuzzy controller for each region. Therefore, this proposed condition is less conservative. The piecewise Lyapunov stability criterion is expressed in terms of Linear Matrix Inequalities (LMIs).
The advantages of the piecewise fuzzy regional concept are less conservative, simpler to design and to be realized easily. In addition, this thesis will extend the piecewise Lyapunov stability criterion and the fuzzy region concept to the controller design of system with uncertainty and observer design. The purposes of this thesis are to address the robust fuzzy region control problem and design the observer rules for each fuzzy region such that the overall fuzzy model are stabilized. Furthermore, numerically examples are given to illustrate the usefulness of the proposed approaches.

關鍵字(中)

★ T-S 模糊區域概念
★ 線性矩陣不等式(LMI)
★ 分段Lyapunov穩定準則
★ 模糊區域觀察器

關鍵字(英)

★ piecewise Lyapunov stability criterion
★ Linear Matrix Inequality (LMI)
★ T-S fuzzy region concept
★ fuzzy regional observer

論文目次

目錄I
圖目錄III
第一章緒論
1.1背景與動機1
1.2文獻回顧與目的3
1.3論文架構4
第二章T-S模糊系統之建構與問題描述
2.1簡介5
2.2離散T-S模糊系統分析與設計5
2.2.1離散T-S模糊系統5
2.2.2離散T-S模糊系統穩定分析7
2.3離散T-S模糊區域系統分析與設計10
2.3.1離散T-S模糊區域系統10
2.3.2離散T-S模糊區域系統穩定分析13
2.4問題描述15
第三章模糊系統之分段控制
3.1簡介16
3.2分段Lyapunov穩定準則16
3.3模糊區域系統之分段控制18
3.4系統模擬21
3.4.1分段區域數值模擬21
3.4.2數值例子比較26
第四章不確定系統之分段區域控制
4.1簡介32
4.2不確定系統之T-S模糊控制器設計32
4.3不確定系統之分段區域控制器設計35
4.4系統模擬40
第五章分段區域觀察器之分析與設計
5.1簡介45
5.2系統背景及問題描述45
5.3分段區域概念之觀察器設計49
5.4系統模擬53
第六章結論與未來展望60
參考文獻61
論文著作64

參考文獻

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指導教授

鍾鴻源(Hung-Yuan Chung)

審核日期

2007-6-27

推文