齊次多項式尤拉法應用於切換式模糊觀測器設計

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巴宇平(Yu-Ping Ba) 查詢紙本館藏

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機械工程學系

論文名稱

齊次多項式尤拉法應用於切換式模糊觀測器設計
(Piecewise Fuzzy Observer Design - Homogeneous Polynomial Lyapunov Euler Method)

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摘要(中)

本論文主要研究連續模糊系統之非二次穩定(non-quadratic stability)
條件下的片段式李亞普諾夫函數，再加入切換式觀測器去提升
追蹤狀態的效能。藉由改變穩定度條件裡的變數，使數個李亞普諾
夫函數得以交錯，重新組成一片段式李亞普諾夫函數，其中皆以尤拉
齊次多項式定理建立非二次李亞普諾夫函數(non-quadratic Lyapunov
function)，其形式為
V (x) = xTP(x)x = 1
g(g??1)xT?xxV (x)x。
然後再使用求得的李亞普諾夫函數之交錯時間點去設計切換式觀
測器，在設計切換式觀測器的過程中，也去探討不同類型的系統(系
統矩陣是否包含待估測狀態)，所需的觀測器格式與穩定度條件。
例題模擬部分，先以泰勒級數建模得出模糊系統，且以非二次的
李亞普諾夫函數及對時間的變化率作為穩定的條件，加入片段式結構
後，再以平方和方法(Sum-of-Squares) 來檢驗模糊系統的穩定條件，
並設計出合適的切換式觀測器。

摘要(英)

The main contribution in this thesis is Piecewise-Lyapunov-Function-
Based Switching Fuzzy Observer with non-quadratic stability for continuous
fuzzy system. At first, we consider several non-quadratic Lyapunov
function with form designed as
V (x) = xTP(x)x = 1
g(g??1)xT?xxV (x)x.
Then, we combine these Lyapunov functions into one Piecewise-
Lyapunov-Function by the parameter, , and design the Switching Observer
by using the crossing point forming Piecewise-Lyapunov-Function.
At the same time, we investigate the stable condition with different type
fuzzy system.
In numerical simulation, we solve for Piecewise-Lyapunov-Function-
Based Switching Fuzzy Observer with sum-of-squares approach.

關鍵字(中)

★ Takagi-Sugeno 模糊系統
★ 片段式李亞普諾夫函數
★ 切換式觀測器
★ 非二次穩定
★ 平方和
★ 尤拉齊次多項式定理
★ 泰勒級數

關鍵字(英)

★ T-S fuzzy systems
★ Piecewise Lyapunov function
★ Switching observer
★ Non-quadratic stability
★ Sum of squares
★ Euler’s Theorem for Homogeneous Functions
★ Taylor-Series

論文目次

中文摘要 i
英文摘要 ii
謝誌 iii
目錄 iv
圖目錄 vi
1、背景介紹 1
1.1 文獻回顧 1
1.2 研究動機 2
1.3 論文結構 4
1.4 符號標記 4
1.5 預備定理 5
2、系統架構與檢測條件 7
2.1 模糊系統與模糊觀測系統架構 7
2.2 尤拉齊次多項式定理 11
2.3 片段式李亞普諾夫函數 15
2.4 片段式齊次李亞普諾夫函數與切換式模糊觀測器 18
2.5 穩定度條件 20
3、模糊建模方法及平方和檢測法 32
3.1 泰勒級數模糊 32
3.2 平方和檢驗法 35
3.3 平方和檢驗法之片段式齊次李亞諾夫觀測系統 38
4、電腦模擬 43
4.1 例題一 43
4.2 例題二 59
4.3 例題三 74
4.4 例題四 94
5、結論與未來方向 108
5.1 結論 108
5.2 未來研究方向 109
文獻 110

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115

指導教授

羅吉昌(J.C Lo)

審核日期

2017-8-25

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