博碩士論文 101323094 詳細資訊




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姓名 章為盛(Wei-sheng Chang)  查詢紙本館藏   畢業系所 機械工程學系
論文名稱 平方和模糊系統觀測器設計 -齊次多項式法
(SOS-Based Fuzzy Observer Dsigns -Homogeneous Polynomial Approach)
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摘要(中) 本論文主要研究連續及離散模糊觀測系統的非二次穩定
(Non-quadratic stability) 條件,關於擴展狀態決定於非二次李亞普諾
夫函數,其函數形式是V(e)=1/2e^TQ(e)e,其中條件Q(e)> 0 取決於Q(e)
是一正定的梯度向量(gradient vector)。遺憾的是,此梯度向量Q(e)
是一非凸面體(nonconvex) 的問題,因此可觀測的模糊系統
之穩定性檢測條件,需要使用尤拉齊次多項式定理,並使用其定理之
齊次性質,以平方和方法(Sum of squares) 去檢驗非凸面體問題,使
得其模擬系統之空間解更佳。最後,模擬其多項式模糊系統,表現出
本論文提出之方法是有效的。
摘要(英) In this thesis, we extend of the state dependent Riccati inequalities to non-quadratic Lyapunov function of the form V (e) = 1/2e^TQ(e)e where Q(e) > 0 requires that Q(e) is a gradient of positive definite function.Unfortunately, the test of Q(e) is nonconvex problem. Thus this thesis studies stabilization problems of the polynomial fuzzy systems via homogeneous Lyapunov functions exploiting the Euler’s homogeneity property to construct a family of SOS polynomials that solves the nonconvexity problem and releases conservatism as well. Lastly, examples of polynomial fuzzy systems are demonstrated to show the proposed
method being effective and effective.
關鍵字(中) ★ 非二次穩定
★ 平方和
★ 參數相依齊次多項式
★ 模糊系統
★ 尤拉齊次多項式定理
關鍵字(英) ★ Non-quadratic stability
★ Sum of squares
★ Homogeneous polynomially parameter-dependent (HPPD) functions
★ T-S fuzzy systems
★ 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、 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 . . . . . . . . . . . . . . . . . . . . . . . 3
1.5 預備定理 . . . . . . . . . . . . . . . . . . . . . . . 5
二、 連續及離散系統架構與檢測條件............................. 7
2.1 連續系統架構 . . . . . . . . . . . . . . . . . . . . . 7
2.2 連續模糊系統之檢測條件(一) . . . . . . . . . . . 9
2.3 尤拉齊次多項式定理 . . . . . . . . . . . . . . . . . 12
2.4 連續模糊系統之檢測條件(二) . . . . . . . . . . . 13
2.5 離散系統架構 . . . . . . . . . . . . . . . . . . . . . 17
2.6 離散模糊系統之檢測條件 . . . . . . . . . . . . . . . 19
三、 平方和檢測條件........................................ 23
3.1 平方和檢測法 . . . . . . . . . . . . . . . . . . . . . 23
3.2 連續系統平方和檢測條件 . . . . . . . . . . . . . . . 24
3.3 離散系統平方和檢測條件 . . . . . . . . . . . . . . . 25
四、 電腦模擬............................................. 27
4.1 模擬題目(一) . . . . . . . . . . . . . . . . . . . . 27
4.2 模擬題目(二) . . . . . . . . . . . . . . . . . . . . 38
4.3 模擬題目(三) . . . . . . . . . . . . . . . . . . . . 48
4.4 模擬題目(四) . . . . . . . . . . . . . . . . . . . . 51
4.5 模擬題目(五) . . . . . . . . . . . . . . . . . . . . 54
4.6 模擬題目(六) . . . . . . . . . . . . . . . . . . . . 57
五、 結論與未來方向........................................ 60
5.1 結論 . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2 未來研究方向 . . . . . . . . . . . . . . . . . . . . . 61
附錄一 .................................................. 62
A.1 波雅定理 . . . . . . . . . . . . . . . . . . . . . . 62
參考文獻................................................. 63
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指導教授 羅吉昌(Ji-Chang Lo) 審核日期 2014-7-28
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