耗散性估測器-波雅定理

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吳東陵(Dong-Lin Wu) 查詢紙本館藏

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機械工程學系

論文名稱

耗散性估測器-波雅定理
(Dissipative Filtering-Polya's theorem)

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摘要(中)

本論文是研究模糊系統 (fuzzy systems)所代表的非線性系統之估測問題,並且藉由耗散性的探討,來描述一廣義之性能指標 ,以及應用波雅定理 (Pólya’s theorem)於檢測條件上 ,來得到一較為寬鬆的檢測條件。內容方面本論文將分為兩部分來進行討論 ,第一部份先推導滿足耗散性的檢測條件,第二部分代入波雅定理的概念 ,來加以求解第一部分的 LMIs。
本論文將在 LMI(LinearMatrixInequality)中探討一個新的降低保守性的檢測條件,連續及離散模糊系統將由統一的方法來論述。藉由建立在李亞普諾夫函數 (Lyapunov function)及參數相依齊次多項式-LMIs(HomogeneousPolynomialParameterDependent-LMIs)解之結構的概念 ,可設計一高次齊次多項式矩陣解滿足 LMI,即待求的估測器增益不必為一次式 ,而可以是一高次齊次式增益,來加以估測,在求解檢測條件方面,代入波雅定理,降低檢測條件的保守性,以求得較佳的解。
本論文同時也研究估測一非線性系統之某些狀態並滿足所要求的性能,首先將此非線性系統以 Takagi-Sugeno(T-S)模糊系統來描述之,以提供一套系統化的研究方法 ,研究非線性系統與估測系統所組成的估測誤差系統的穩定性與性能的分析問題。針對 T-S模糊模型,本論文根據 HPPD-LMI的概念設計一高次齊次多項式矩陣估測器,並探討估測誤差系統是否滿足耗散性,最後代入波雅定理探討求解的檢測條件,進而達到共同 P二次李亞普諾夫穩定的充要條件。

摘要(英)

A new stabilization condition guaranteeing dissipativity of T-S fuzzy filtering error systems is studied in this paper,
continuous- and discrete-time fuzzy filtering error systems treated in a unified manner.
A premise-dependent HPPD gain (i.e., grade of membership, μ) is considered.
The stabilization and performance analysis is performed on the basis of dissipativity,
here stated using LMI to profit from the advantage of convex optimization.
Using Pólya’’s theorem, we can see the reduction of conservative, such that the performance get more and more better.
It is shown, via theoretical analysis and numerical simulations, that our results are much
less conservative via Pólya’’s theorem.

關鍵字(中)

★ 波雅定理
★ 耗散性
★ 估測器

關鍵字(英)

★ Polya's theorem
★ dissipative
★ filter

論文目次

目錄
論文摘要 I
誌謝 IV
圖目 VIII
第一章簡介 1
1.1文獻回顧 ························· 1
1.2研究動機 ························· 3
1.3論文結構 ························· 3
1.4符號標記 ························· 4
1.5預備定理 ························· 4
第二章系統數學模型 6
2.1系統的數學模型 ····················· 6
2.2估測器的數學模型 ···················· 7
2.2.1 Case A :獨立於估測的狀態變數 ··········· 8
2.2.2 Case B :相依於估測的狀態變數 ··········· 13
第三章耗散性–估測器 15
3.1耗散性定義 ······················· 15
3.2 CaseA :獨立於估測的狀態變數 ············ 18
3.2.1連續系統 ······················· 18
3.2.2離散系統 ······················· 22
3.3 CaseB :相依於估測的狀態變數 ············ 24
3.3.1連續系統 ······················· 24
3.3.2離散系統 ······················· 27
第四章電腦模擬 30
4.1 Case A連續例子 ···················· 30
4.1.1估測器設計與求解-連續系統(CaseA) ········ 33
4.2 Case B離散例子 ···················· 38
4.2.1估測器設計與求解-離散系統 (Case B) ······· 39
第五章波雅定理之應用 45
5.1波雅定理 ························· 46
5.2 CaseA :獨立於估測的狀態變數 ············ 48
5.2.1連續系統 ······················· 48
5.2.2離散系統 ······················· 51
5.3 CaseB :相依於估測的狀態變數 ············ 53
5.3.1連續系統 ······················· 53
5.3.2離散系統 ······················· 55
第六章電腦模擬 58
6.1 Case A離散例子 ···················· 58
6.1.1估測器設計與求解-離散系統(CaseA)········· 59
6.2 Case B離散例子 ···················· 60
6.2.1估測器求解-離散系統 (Case B) ············ 60
第七章結論與未來發展 62
7.1總結 ··························· 62
7.2未來研究 ························· 63
參考文獻 64

參考文獻

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指導教授

羅吉昌(Ji-Chang Lo)

審核日期

2008-6-24

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