齊次多項式尤拉法應用於切換式模糊控制器設計

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姓名

戴均維(Jun-Wei Tai) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

齊次多項式尤拉法應用於切換式模糊控制器設計
(Piecewise Fuzzy Controller Design—Homogeneous Polynomial Lyapunov Euler Method)

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摘要(中)

本論文主要研究齊次多項式尤拉法應用於切換式模糊控制器設計，以泰勒級數建模產生模糊系統，並使用片段式李亞普諾夫函數(piecewise polynomial Lyapunov function) 作穩定性分析，其高階李亞普夫函數型式為V (x) = min_1<=l<=N(V_l(x))，其中V_l(x)=x^T*P_l(x)*x，N 為分段個數，根據dot(V(x))<0，做穩定性條件分析，在求解的過程中，片段李亞普諾夫函數V_l(x) 對時間微分會產生Pl(x) 之微分項，其化簡過程過於繁瑣複雜，為避免此問題，引用尤拉齊次法，再以平方和方法檢驗穩定度條件，並設計出控制器。

摘要(英)

In this thesis, it is mainly to research piecewise fuzzy controller design by homogeneous polynomial Lyapunov Euler method. We use Taylor series to model the fuzzy system, and implement the analysis of stability by piecewise polynomial Lyapunov function,which has the following form:V(x)= min_1<=l<=N(V_l(x))and V_l(x)=x^T*P_l(x)*x. Due to the fact that dot(V_l(x))=dot(x_T)*P_l(x)*x+x^T*dot(P_l(x))*x+x^T*P_l(x)*dot(x), the dot(P_l(x)) will yields complicated form to implement stablility condition. To avoid this problem, we propose a homogeneous polynomial function method and utilize Euler’s theorem for homogeneous function. The next, we solve the stabilization problem under consideration by the method of sum of squares and design its corresponding controller.

關鍵字(中)

★ 非二次穩定
★ 平方和
★ Takagi-Sugeno 模糊系統
★ 尤拉齊次多項式定理
★ 片段多項式李亞普諾夫函數

關鍵字(英)

★ non-quadratic stability
★ sum of squares
★ T-S fuzzy systems
★ Euler’s Theorem for Homogeneous Function
★ piecewise polynomial Lyapunov function

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、系統架構與穩定度檢測條件. 7
2-1 連續模糊系統架構與模糊規則. 7
2-2 尤拉齊次關係式. 8
2-3 S-procedure 11
2-4 最小型式片段李亞普諾夫函數. 12
2-5 最小型式片段齊次李亞普諾夫函數之控制器設
計之穩定條件. 13
3、模糊建模方法及平方和檢測法. 18
3-1 泰勒級數模糊. 18
3-2 平方和檢驗法. 20
3-3 平方和檢驗法之定理2.1 穩定度條件. 23
4、電腦模擬. 26
4-1 例題一. 26
4-2 例題二. 40
4-3 例題三. 54
5、結論與未來方向. 71
5-1 結論. 71
5-2 未來方向. 72
參考文獻. 73

參考文獻

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指導教授

羅吉昌(Ji-Chang Lo)

審核日期

2017-8-23

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