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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 Feedback linearization ： ウィキペディア英語版 Feedback linearization Feedback linearization is a common approach used in controlling nonlinear systems. The approach involves coming up with a transformation of the nonlinear system into an equivalent linear system through a change of variables and a suitable control input. Feedback linearization may be applied to nonlinear systems of the form : y &= h(x) \qquad \qquad \qquad &(2)\end where $x\; \backslash in\; \backslash mathbb^n$ is the state vector, $u\; \backslash in\; \backslash mathbb^p$ is the vector of inputs, and $y\; \backslash in\; \backslash mathbb^m$ is the vector of outputs. The goal is to develop a control input :$u\; =\; a(x)\; +\; b(x)v\backslash ,$ that renders a linear input–output map between the new input $v$ and the output. An outer-loop control strategy for the resulting linear control system can then be applied. == Feedback Linearization of SISO Systems == Here, we consider the case of feedback linearization of a single-input single-output (SISO) system. Similar results can be extended to multiple-input multiple-output (MIMO) systems. In this case, $u\; \backslash in\; \backslash mathbb$ and $y\; \backslash in\; \backslash mathbb$. We wish to find a coordinate transformation $z\; =\; T(x)$ that transforms our system (1) into the so-called normal form which will reveal a feedback law of the form :$u\; =\; a(x)\; +\; b(x)v\backslash ,$ that will render a linear input–output map from the new input $v\; \backslash in\; \backslash mathbb$ to the output $y$. To ensure that the transformed system is an equivalent representation of the original system, the transformation must be a diffeomorphism. That is, the transformation must not only be invertible (i.e., bijective), but both the transformation and its inverse must be smooth so that differentiability in the original coordinate system is preserved in the new coordinate system. In practice, the transformation can be only locally diffeomorphic, but the linearization results only hold in this smaller region. We require several tools before we can solve this problem. 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「Feedback linearization」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.