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    Title: 利用漢米爾敦象統中的基本限制來進行導航不確定性的控制
    Other Titles: Uncertainty Control Utilizing Natural Dynamics in Hamiltonian Systems
    Authors: 蕭富元;曾仁宏
    Contributors: 淡江大學航空太空工程學系
    Keywords: 漢米爾敦系統;不可擠壓理論;不確定性;控制
    Date: 2006-03
    Issue Date: 2010-01-11 15:12:27 (UTC+8)
    Publisher: 臺北縣淡水鎮:淡江大學
    Abstract: 本文在探討;其米爾敦系統(Hamiltonian Systems) 中,關於Gromov 的“不可擠壓理論" (Non-squeezing Theorem)在不確定性分析及控制的應用性。該理論闡述了一項有關symplectic 流形(manifolds) 的基本特性;然而,它卻常常以抽象的拓撲學方式呈現出來,因此實際的物理意義仍有待釐清。在本文中,我們將該理論實用化:對於一個正值且對稱的矩陣(Positive-definite , symmetric matrix) ,我們可以定義出“線性辛寬度" (linear simplectic width)的物理意義,而該項正是由不可擠壓理論所導出的~統下限。對於一個實際的動力系統,正值且對稱的短陣通常被用來代表系統的不確定性棉球,因此我們的結果剛好可以應用於實際問題的分析。在我們的研究成果裡'我們推導出一則關於不確定性演化的不等式,並且將之運用於系統的不確定性分析及控制上。我們也提供一些數值模擬作為驗證及參考。
    A realization of Gromov's nonsqueezing theorem and its applications to uncertainty analysis in Hamiltonian systems are studied in this paper. Gromov's nonsqueezing theorem describes a fundamental property of symplectic manifolds, however, this theorem is usually started in terms of topology and its physical meaning is vague. In this paper we introduce a physical interpretation of the linear symplectic width, which is the lower bound in the nonsqueezing theorem, given the igenstructure of a positivedefinite, symmetric matrix. Since a positivedefinite, symmetric matrix always represents the uncertainty ellipsoid in practical mechanics problems, our study can be applied to uncertainty analysis. We fmd a fundamental inequality for the evolving uncertainty in a linear dynamical system and provide some numerical examples.
    Relation: 第五屆海峽兩岸航空太空學術研討會論文集, pp.357-366
    Appears in Collections:[航空太空工程學系暨研究所] 會議論文

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