連續模糊控制系統之非二次穩定性分析

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姓名

李家洪(Jia-hong Li) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

連續模糊控制系統之非二次穩定性分析
(Stabilization Analysis for Non-quadratic Continuous-time Fuzzy Control Systems)

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摘要(中)

本篇論文主要研究連續時間強健 (Robust) 控制系統及連續時間 Takagi-Sugeno(T-S)模糊控制系統的非二次(non-quadratic)穩定寬鬆條件; 我們利用波雅定理(Polya Theorem)的代數性質加上寬鬆矩陣變數(slack matrix variables)來建立一組寬鬆的線性矩陣不等式(LMI)，因為非二次(non-quadratic)穩定的分析加上寬鬆矩陣變數 (slack matrix variables) 的使用，使得此組線性矩陣不等式(LMI)的求解保守性更進一步的降低，亦即當使用波雅定理(Polya Theorem)時，齊次多項式的階數不用太高，就可以找到解，這是本論文最大的優點；最後會提出幾個例子來證明我們理論的優越性。
關鍵字：強健(Robust)控制系統 Takagi-Sugeno(T-S)模糊控制系統、非二次 (non-quadratic)穩定、波雅定理 (Polya Theorem)、寬鬆矩陣變數(slack matrix variables)、線性矩陣不等式 (LMI)

摘要(英)

In this thesis, we investigate non-quadratic ralaxation for continuous-time robust control systems
and continuous-time fuzzy control systems, which are characterized by parameter-dependent LMIs (PD-LMIs), exploiting
the algebraic property of Polya Theorem to construct a family of finite-dimensional LMI relaxations with righ-hand-side
slack matrices that release conservatism. Lastly, numerical
experiments to illustrate the advantage of relaxations, being less conservative and effective, are provided.
it keyword: Robust control systems; Takagi-Sugeno fuzzy control systems; Non-quadratic relaxations;
Parameter-dependent LMIs (PD-LMIs); Polya Theorem; Slack matrices; Linear matrix inequality (LMI).

關鍵字(中)

★ 強健控制系統
★ 線性矩陣不等式
★ 模糊控制
★ 非二次穩定性分析
★ 寬鬆矩陣變數

關鍵字(英)

★ non-quadratic
★ Takagi-Sugeno(T-S)
★ LMI
★ slack matrix variables

論文目次

中文摘要 i
英文摘要 ii
謝誌 iii
一、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...7
二、連續強健閉迴路系統之寬鬆穩定條件... 8
2.1控制系統的架構...8
2.2波雅定理(Polya Theorem) ...8
2.3連續強健閉迴路系統之穩定條件...9
2.3.1 使用共同李亞普若夫函數 ...9
2.3.2 使用非共同李亞普若夫函數 ...10
iv
2.3.3 非共同李亞普若夫函數結合寬鬆矩陣變數...16
三、強健系統電腦模擬...23
3.1 例子　１...23
3.2 例子　２...25
3.3 例子　３ ...30
四、連續模糊閉迴路系統之寬鬆穩定條件... 35
4.1 控制系統的架構...35
4.2 連續模糊閉迴路系統之穩定條件...35
4.2.1 使用共同李亞普若夫函數...36
4.2.2 使用非共同李亞普若夫函數 ...38
4.2.3 非共同李亞普若夫函數結合寬鬆矩陣變數 ...41
五、模糊系統電腦模擬...46
5.1 例子　１ ...46
5.2 例子　２ ...51
5.3 例子　３...58
六、結論與未來方向 ... 64
6.1 結論 ...64
6.2 未來方向 ...65
參考文獻 ... 66

參考文獻

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指導教授

羅吉昌(Ji-Chang Lo)

審核日期

2012-7-24

推文