齊次多項式 H∞ 靜態輸出回授控制 -連續/離散系統

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姓名

楊宇軒(Yu-Xuan Yang) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

齊次多項式 H∞ 靜態輸出回授控制 -連續/離散系統
(Polynomially Static Output Feedback H∞ Control via Homogeneous Lyapunov Functions for Continuous- and Discrete-time Systems)

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摘要(中)

本論文主要研究多項式模糊系統之靜態輸出回授控制器設計，使用齊次多項式李亞普諾夫函數 (Lyapunov function) 及其對時間的導數作為穩定條件，並同時滿足 H∞ 性能指標。本論文研究靜態輸出回授是因為它比狀態回授能夠更廣泛的應用到實務上，而靜態輸出回授增益設計，分別探討連續以及離散系統。連續系統中利用尤拉齊次多項式定理建立李亞普諾夫函數 (Lyapunov function)，其形式為
V (x) = xT P (x)x = 1 xT ?xxV (x)x g(g ? 1)
離散系統為避免非二次齊次多項式李亞普諾夫函數 (Lyapunov function) 在其中發生問題，在本論文中將令李亞普諾夫函數 (Lyapunov function) 為
V ( x ) = x T P ? 1 ( x ? ) x
其中 x ? 為系統狀態向量 x 裡不直接被控制器影響的系統狀態集合而成。此限制可使後續電腦模擬時可行，內文中將詳細說明。
電腦模擬方面以平方和方法 (Sum-of-Squares) 來檢驗模糊系統的穩定條件，並設計靜態輸出回授控制器。

摘要(英)

In this thesis, we investigate H∞ control problem for both continuous- and discrete-time polynomial fuzzy systems, and to design static output feed- back controllers. The stabilization of the underlying systems can be proved via homogeneous Lyapunov method. This thesis studies static output feed- back control that is more appropriate in practical than state feedback con- trol. In continuous-time systems, Euler’s homogeneous polynomial theorem is used to formulate a Lyapunov function. It has the following form
V (x) = xT P (x)x = 1 xT ?xxV (x)x g(g ? 1)
In discrete-time systems, the Lyapunov function is formulated by
V ( x ) = x T P ? 1 ( x ? ) x
where x ? are part of x that are not directly affected by the control input. This restriction is to avoid problems when doing simulation. The details will be described later.
In numerical simulations, examples are solved via the sum-of-squares approach.

關鍵字(中)

★ 平方和
★ 多項式模糊系統
★ 尤拉齊次多項式定理
★ H_∞ 靜態輸出回授控制

關鍵字(英)

★ Sum of squares
★ Polynomial fuzzy systems
★ Euler’s theorem
★ H_∞ static output feedback control

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 ........................ 3
1.4 符號標記 ........................ 4
1.5 預備定理 ........................ 5
2、系統架構與主要定理........................................................... 9
2.1 模糊系統架構簡介................... 9
2.2 H∞靜態輸出回授控制系統 .............. 10
2.3 主要定理 . . . . . . . . . . . . . . . . . . . . . . . . 15
3、模糊建模方法及平方和檢測法........................................... 23
3.1 泰勒級數模糊 . . . . . . . . . . . . . . . . . . . . . . 23
3.2 平方和檢驗法 . . . . . . . . . . . . . . . . . . . . . . 25
4、電腦模擬............................................................................... 29
4.1 例題一..........................29
4.2 例題二..........................37
4.3 例題三..........................43
4.4 例題四..........................51
4.5 例題五..........................55
5、結論與未來方向................................................................... 59
5.1 結論 . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2未來研究方向 . . . . . . . . . . . . . . . . . . . . . . 60
參考文獻..................................................................................................... 61

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指導教授

羅吉昌(Ji-Chang Lo)

審核日期

2018-8-15

推文