臺灣博碩士論文加值系統

本論文主要探討半線性拋物線分布參數系統在逐點控制及指數穩定問題。首先，我們考慮一個以非線性拋物線型偏微分方程系統表示之分布參數系統，利用泰勒級數建模方法建模成一個多項式模糊拋物線偏微分系統。此外，針對多項式模糊拋物線偏微分系統設計三種不同狀態回授之模糊控制器，分別為全狀態回授、逐點狀態回授以及並列逐點狀態回授。而在穩定性分析的部分，我們利用多項式李亞普諾夫函數、尤拉齊次關係式及向量值Wirtinger不等式，推導出三個以平方和形式的指數穩定條件。最後，以一實際物理系統以及一個數值範例，驗證我們所提出方法之可行性及有效性。

In this thesis, the problems of pointwise control design and exponential stabilization for the semilinear parabolic distributed parameter systems are investigated. Firstly, a distributed parameter system which is expressed by the nonlinear parabolic partial differential equation (PDE) system is modeled as a polynomial fuzzy parabolic PDE system by Taylor’s series identification approach. For controller design, three kinds of fuzzy controllers are designed for the polynomial fuzzy parabolic PDE system including full state feedback, pointwise state feedback, and collocated pointwise state feedback. By examining the stability analysis, based on the homogeneous polynomial Lyapunov function, Euler＇s homogeneous relation, and vector-valued Wirtinger's inequality, three different exponential stabilization conditions are proposed in terms of sum-of-squares (SOS). Lastly, a physical system and a numerical example are illustrated to show the feasibility and validity of the proposed methods.

目錄
中文摘要 i
英文摘要 ii
誌謝 iii
目錄 iv
圖目錄 v
第一章緒論 1
1.1 前言 1
1.2 研究動機與目的 2
1.3 論文架構 3
1.4 符號標記 4
1.5 輔助定理 4
第二章半線性拋物線偏微分方程系統 8
2.1 系統架構 8
2.2 多項式模糊偏微分方程模型 9
第三章狀態回授控制器設計與穩定性分析 11
3.1 多項式模糊狀態回授控制器 11
3.2 全狀態回授(Full state feedback) 12
3.3 逐點狀態回授(Pointwise state feedback) 18
3.4 並列逐點狀態回授(Collocated pointwise state feedback) 22
第四章電腦模擬 28
4.1 範例1 28
4.1.1 全狀態回授 31
4.1.2 逐點狀態回授 33
4.1.3 並列逐點狀態回授 35
4.2 範例2 37
4.2.1 全狀態回授 40
4.2.2 逐點狀態回授 42
4.2.3 並列逐點狀態回授 44
第五章結論及未來展望 46
參考文獻 47

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