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.
