H∞模糊系統控制-寬鬆變數法

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姓名

鄭丞謨(Cheng-Mo Zheng) 查詢紙本館藏

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機械工程學系

論文名稱

H∞模糊系統控制-寬鬆變數法
(H∞ satbilition analysis for fuzzy control system)

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摘要(中)

本篇論文是研究狀態回饋控制以及 H∞ 性能的模糊控制穩定性分析，本論文將分成兩部分來進行討論，
第一部份先推導(控制)系統滿足 Lyapunov 穩定的檢測條件。
第二部分考慮干擾的影響，推導出使受控系統滿足 H∞ 穩定的檢測條件。
對於一個具非線性特徵的 Takagi-Sugeno(T-S) 模糊系統，在新的寬鬆充分條件之下保證其穩定。
無論是連續或者離散時間的模糊(控制)系統都是用相似的方法(檢測條件 LMIs)來探討。
本篇論文是針對一個前件部相依的 Lyapunov 函數(premise-dependent Lyapunov function)來探討 T-S 模糊系統的穩定條件，
而以前的文獻一般都是用單一矩陣 P(common P) 來推導所需的檢測條件。
對於穩定與性能分析以及控制器的設計目前都是用 LMI 以及數值分析來處理運算，
這些採用前件部相依的 Lyapunov 函數(premise-dependent Lyapunov function)
經數理證明及電腦模擬的結果都比現存文獻採用單一矩陣 P(common P) 的結果寬鬆。

摘要(英)

In this paper, sufficient LMI conditions for the H∞ state feedback
control synthesis of fuzzy control systems consisting of Takagi-Sugeno
fuzzy models are proposed for continuous- and discrete-time fuzzy sys-
tem in a unified manner. Based on a premise-dependent Lyapunov func-
tion, we release the conservatism that commonly exists in the common
P approach. Particularly, the restriction embedded in continuous-time
systems on derivative of μ is removed by introducing Lie derivative to
the Lyapunov approach. It is shown that the slack variables employed in
this paper provide additional feasibility in solving the H∞ stabilization
problem of fuzzy control systems. Consequently, the stabilization condi-
tions are shown to be more relaxed than others in the existing literature.
Numerical simulations appear promising for the proposed method and
illuminate the reduction of conservatism clearly.

關鍵字(中)

★ 模糊系統

關鍵字(英)

★ fuzzy

論文目次

論文摘要 I
致謝 III
圖目 VII
第一章簡介 1
1.1 文獻回顧 1
1.2 研究動機 2
1.3 論文結構 3
1.4 符號標記 4
1.5 預備定理 4
1.6 線積分模糊Lyapunov 函數 7
第二章系統架構與穩定條件 10
2.1 系統架構 10
2.2 共同P檢測條件 11
2.3 非共同P檢測條件 12
第三章控制系統架構與穩定條件 20
3.1 控制系統架構 20
3.2共同P檢測條件 21
3.3非共同P檢測條件 22
第四章電腦模擬：控制系統 29
4.1純系統 29
4.2 連續控制系統 34
4.3 離散控制系統 38
第五章系統架構與H∞定理 42
5.1 H∞定理 42
5.2 數學模型 43
5.3共同P檢測條件 44
5.4非共同P檢測條件 47
第六章電腦模擬：控制與性能 61
6.1 H∞ 連續系統 61
6.2 H∞ 離散系統 67
第七章總結與未來研究方向 69
7. 總結 69
7. 未來研究方向 70
參考文獻 71

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指導教授

羅吉昌(Ji-Chang Lo)

審核日期

2006-6-30

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