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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Orbit (control theory) ： ウィキペディア英語版 Orbit (control theory) The notion of orbit of a control system used in mathematical control theory is a particular case of the notion of orbit in group theory. ==Definition== Let $\backslash dot\; q=f(q,u)$ be a $\backslash \; ^\backslash infty$ control system, where $$ belongs to a finite-dimensional manifold $\backslash \; M$ and $\backslash \; u$ belongs to a control set $\backslash \; U$. Consider the family $=\backslash$ and assume that every vector field in $$ is complete. For every $f\backslash in$ and every real $\backslash \; t$, denote by $\backslash \; e^$ the flow of $\backslash \; f$ at time $\backslash \; t$. The orbit of the control system $\backslash dot\; q=f(q,u)$ through a point $q\_0\backslash in\; M$ is the subset $\_$ of $\backslash \; M$ defined by :$\_=\backslash \; f\_\}\backslash circ\backslash cdots\backslash circ\; e^(q\_0)\backslash mid\; k\backslash in\backslash mathbb,\backslash \; t\_1,\backslash dots,t\_k\backslash in\backslash mathbb,\backslash \; f\_1,\backslash dots,f\_k\backslash in\backslash \}.$ ;Remarks The difference between orbits and attainable sets is that, whereas for attainable sets only forward-in-time motions are allowed, both forward and backward motions are permitted for orbits. In particular, if the family $$ is symmetric (i.e., $f\backslash in$ if and only if $-f\backslash in$), then orbits and attainable sets coincide. The hypothesis that every vector field of $$ is complete simplifies the notations but can be dropped. In this case one has to replace flows of vector fields by local versions of them. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Orbit (control theory)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.