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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 Flat pseudospectral method ： ウィキペディア英語版 Flat pseudospectral method The flat pseudospectral method is part of the family of the Ross–Fahroo pseudospectral methods introduced by Ross and Fahroo.〔 Ross, I. M. and Fahroo, F., “Pseudospectral Methods for the Optimal Motion Planning of Differentially Flat Systems,” IEEE Transactions on Automatic Control, Vol.49, No.8, pp. 1410–1413, August 2004.〕 〔 Ross, I. M. and Fahroo, F., “A Unified Framework for Real-Time Optimal Control,” Proceedings of the IEEE Conference on Decision and Control, Maui, HI, December, 2003.〕 The method combines the concept of differential flatness〔 Fliess, M., Lévine, J., Martin, Ph., and Rouchon, P., “Flatness and defect of nonlinear systems: Introductory theory and examples,” International Journal of Control, vol. 61, no. 6, pp. 1327–1361, 1995. 〕 〔 Rathinam, M. and Murray, R. M., “Configuration flatness of Lagrangian systems underactuated by one control” SIAM Journal on Control and Optimization, 36, 164,1998. 〕 with pseudospectral method to generate outputs in the so-called flat space. ==Concept== Because the differentiation matrix, $D$, in a pseudospectral method is square, higher-order derivatives of any polynomial, $y$, can be obtained by powers of $D$, : $$ \begin \dot y &= D Y \\ \ddot y & = D^2 Y \\ & where $Y$ is the pseudospectral variable and $\backslash beta$ is a finite positive integer. By differential flatness, there exists functions $a$ and $b$ such that the state and control variables can be written as, : $$ \begin x & = a(y, \dot y, \ldots, y^) \\ u & = b(y, \dot y, \ldots, y^) \end The combination of these concepts generates the flat pseudospectral method; that is, x and u are written as, :$x\; =\; a(Y,\; D\; Y,\; \backslash ldots,\; D^\backslash beta\; Y)$ :$u\; =\; b(Y,\; D\; Y,\; \backslash ldots,\; D^Y)$ Thus, an optimal control problem can be quickly and easiy transformed to a problem with just the Y pseudospectral variable.〔 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「Flat pseudospectral method」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.