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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/11070

Title: 強健穩定性之拓樸分析
Robust Stability Analysis-A Topological Approach
Authors: 鄭智湧
Contributors: NTOU:Department of Electrical Engineering
國立臺灣海洋大學:電機工程學系
Keywords: 拓樸學;結構穩定性;強健穩定性;代數結構
Topology;Structure stability;Robust stability;Algebraic structure
Date: 1996
Issue Date: 2011-06-28T08:08:19Z
Abstract: 自從克里托諾夫定理(Khavitonov theorem)的出現 之後,相關定理的推展及其在強健穩定和強健 控制理論的應用,極點理論(Extreme Point Results)已 成為處理結構化不確定系統(Structured-uncertainty System) 的一項利器.此研究計 劃亦以處理結構化的不確定系統為對象,而以 拓樸學 (Topology)的觀點為出發點,一方面對於傳 統的理論提出拓樸及幾何的新觀點;另一方面 也利用微分及代數拓樸的架構,來研究強健穩 定性問題的結構穩定性 (Structural Stability) 及其 代數結構 (AlgebraicStructure).因此本計劃可歸納 為三具體三方向,包括強健穩定性問題之.bcdot. 古典理論的幾何意義: 對於已存在的極點理論, 給予新的理論觀點及解釋,並藉此尋求新的推 廣 及應用..bcdot.強健控制的結構穩定分析(微 觀局部分析 local analysis):發掘強健控制問題的 結構不穩定現象,找出原因之所在,進而避免其 產生..bcdot.強健控制之代數結構分析(具觀整體 性分析 global analysis): 更深一層地探討強健控 制的代數結構,欲使我們發展更簡易的設計方 法.
Motivated by the Kharitonov theorem and later developed extreme point results, the parametric approach to robust control has been a powerful tool for dealing with structured uncertainty systems. Based on the parametric approach, this proposed research is aimed at providing theoretic as well as computational insights to robust stability problems from a topological viewpoint. On the one hand, we borrowed the concepts from topology and geometry to give extreme point results of robust control a new interpretation; on the other hand, we use the differential and algebraic frameworks to investigate the structural stability and algebraic structures, respectively, of robust stability problems. Three concrete research directions can be summarized as follows: 1. The topological and geometric reinterpretation of extreme point results: we provide new insights to the existing extreme point results; meanwhile, try to extend the theorems to wider applications. 2. The structural stability of robust control problems (local analysis): the goal is to find an explanation for the common phenomenon of structural instability in several robust control problems, and try to resolve it. 3. The algebraic structures of robust control problems (global analysis): investigation on the underlying structures of robust stability problems will be proceeded in order to better understand the design philosophy.
URI: http://ntour.ntou.edu.tw/ir/handle/987654321/11070
Appears in Collections:[電機工程學系] 研究計畫

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