H∞ 連續模糊系統之控制設計-寬鬆穩定條件∞

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陳定穎(Ting-ying Chen) 查詢紙本館藏

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機械工程學系

論文名稱

H∞ 連續模糊系統之控制設計-寬鬆穩定條件∞
(SOS-based H∞ Fuzzy Controller Desging-Relaxation Method)

相關論文

★ 強健性扇形區域穩定範圍之比較	★ 模糊系統混模強健控制
★ T-S模糊模型之建構、強健穩定分析與H2/H∞控制	★ 廣義H2模糊控制-連續系統線性分式轉換法
★ 廣義模糊控制-離散系統線性分式轉換法	★ H∞模糊控制－連續系統線性分式轉換法
★ H∞模糊控制—離散系統線性分式轉換法	★ 強健模糊動態輸出回饋控制-Circle 與 Popov 定理
★ 強健模糊觀測狀態回饋控制-Circle與Popov定理	★ H_infinity 取樣模糊系統的觀測型控制
★ H∞取樣模糊系統控制與觀測定理	★ H-ihfinity取樣模糊系統動態輸出回饋控制
★ H∞模糊系統控制-多凸面法	★ H∞模糊系統控制-寬鬆變數法
★ 時間延遲 T-S 模糊系統之強健 H2/H(Infinity) 控制與估測	★ 寬鬆耗散性模糊控制-波雅定理

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摘要(中)

李亞普諾夫能量函數V (x)對時間t微分會產生Q(x)微分項的
過程，為了要避免這個複雜的問題，則引入尤拉齊次多項式定理，本
論文主要在研究在連續模糊控制系統下的非二次穩定(Non-quadratic
stability)，且加入H1性能指標的觀念，亦即非二次穩定李亞普諾
夫(Lyapunov function)能量函數V (x) = xT adj(Qz(x))x，而藉由尤拉
齊次多項式定理(Euler′s Theorem for Homogeneous Functions)可導
出H1控制之李亞普諾夫不等式檢測穩定矩陣，輔以平方和(Sum of
square)去檢驗其連續模糊系統之穩定條件，最後去模擬例子，來證明
此方法之正確性
i

摘要(英)

Lyapunov energy function V (x) for time dierential will gener-
ate Q(x) process derivative term, in order to avoid this complex is-
sue, the lead to Euler′s homogeneous polynomial theorem, this the-
sis research in continuous fuzzy control system nonquadratic stable
(Non-quadratic stability), and added performance concept of H1 ,
namely non-quadratic Lyapunov stability (Lyapunov function) energy
function V (x) = xT adj(Qz(x))x , and by Euler homogeneous poly-
nomial Theorem (Euler′s Theorem for Homogeneous Functions) can
be exported H1 control of Lyapunov inequality detection stabilizing
matrix, supplemented square and (Sum of square) to test its stability
conditions of continuous fuzzy systems, and nally to simulate exam-
ple, to prove the correctness of this approach
ii

關鍵字(中)

★ 平方和
★ Takagi-Sugeno模糊系統
★ H1控制
★ 非二次穩定
★ 參數相依齊次多項式
★ 尤拉齊次多項式定理

關鍵字(英)

★ Sum of squares
★ T-S fuzzy systems
★ H1 control
★ Non-quadratic stability
★ HPPD
★ Euler′s Theorem for Homogeneous Functions

論文目次

中文摘要.......................................................................................... i
英文摘要.......................................................................................... ii
謝誌................................................................................................. iii
目錄................................................................................................. iv
圖目錄.............................................................................................. vi
一、背景介紹..................................................................... 1
1.1 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究動機. . . . . . . . . . . . . . . . . . . . . . . 3
1.3 論文結構. . . . . . . . . . . . . . . . . . . . . . . 5
1.4 符號標記. . . . . . . . . . . . . . . . . . . . . . . 6
1.5 預備定理. . . . . . . . . . . . . . . . . . . . . . . 8
二、基礎定理..................................................................... 9
2.1 H1 控制定理介紹. . . . . . . . . . . . . . . . . . . 9
2.2 尤拉齊次多項式定理(Euler′s homogeneity theorem) 10
2.3 李亞普諾夫定理(Lyapunov theorem) . . . . . . . . 14
2.4 蕭轉換定理(Schur complement) . . . . . . . . . . . 14
三、連續系統架構..............................................................16
3.1 連續系統架構介紹. . . . . . . . . . . . . . . . . . 16
3.2 連續模糊系統控制加入寬鬆條件之檢測條件. . . . . 17
3.3 H1連續模糊系統控制加入寬鬆條件之檢測條件. . . 22
3.4 建模技巧. . . . . . . . . . . . . . . . . . . . . . . 27
四、平方和檢測條件..........................................................30
4.1 平方和檢驗法. . . . . . . . . . . . . . . . . . . . . 30
4.2 平方和檢驗法之控制連續模糊系統檢測條件. . . . . 33
4.3 平方和檢驗法之H1控制連續模糊系統檢測條件. . . 35
iv
五、Matlab電腦模擬.........................................................38
5.1 例題一. . . . . . . . . . . . . . . . . . . . . . . . . 38
5.2 例題二. . . . . . . . . . . . . . . . . . . . . . . . . 42
5.3 例題三. . . . . . . . . . . . . . . . . . . . . . . . . 47
六、結論與未來方向..........................................................52
6.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.2 未來研究方向. . . . . . . . . . . . . . . . . . . . . 53
附錄一..............................................................................................54
A.1 波雅定理. . . . . . . . . . . . . . . . . . . . . . . 54
A.2 增加激發強度之冪次. . . . . . . . . . . . . . . . 54
A.3 波雅定理之穩定性檢測條件. . . . . . . . . . . . . 56

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指導教授

羅吉昌(Lo, Ji-Chang)

審核日期

2015-7-30

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