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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 Caratheodory-π solution ： ウィキペディア英語版 Caratheodory-π solution A Carathéodory- solution is a generalized solution to an ordinary differential equation. The concept is due to I. Michael Ross and named in honor of Constantin Carathéodory.〔Biles, D. C., and Binding, P. A., “On Carathéodory’s Conditions for the Initial Value Problem," ''Proceedings of the American Mathematical Society,'' Vol. 125, No. 5, May 1997, pp. 1371–1376.〕 Its practicality was demonstrated in 2008 by Ross et al.〔Ross, I. M., Sekhavat, P., Fleming, A. and Gong, Q., "Optimal Feedback Control: Foundations, Examples and Experimental Results for a New Approach," ''Journal of Guidance, Control and Dynamics,'' Vol. 31, No. 2, pp. 307–321, 2008.〕 in a laboratory implementation of the concept. The concept is most useful for implementing feedback controls, particularly those generated by an application of Ross' pseudospectral optimal control theory.〔Ross, I. M. and Karpenko, M. "A Review of Pseudospectral Optimal Control: From Theory to Flight," ''Annual Reviews in Control,'' Vol.36, No.2, pp. 182–197, 2012.〕 ==Mathematical background== A Carathéodory- solution addresses the fundamental problem of defining a solution to a differential equation, :$\backslash dot\; x\; =\; g(x,t)$ when ''g''(''x'',''t'') is not differentiable with respect to ''x''. Such problems arise quite naturally 〔Clarke, F. H., Ledyaev, Y. S., Stern, R. J., and Wolenski, P. R., Nonsmooth Analysis and Control Theory, Springer–Verlag, New York, 1998.〕 in defining the meaning of a solution to a controlled differential equation, :$\backslash dot\; x\; =\; f(x,u)$ when the control, ''u'', is given by a feedback law, :$u\; =\; k(x,t)$ where the function ''k''(''x'',''t'') may be non-smooth with respect to ''x''. Non-smooth feedback controls arise quite often in the study of optimal feedback controls and have been the subject of extensive study going back to the 1960s.〔Pontryagin, L. S., Boltyanskii, V. G., Gramkrelidze, R. V., and Mishchenko, E. F., The Mathematical Theory of Optimal Processes, Wiley, New York, 1962.〕 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「Caratheodory-π solution」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.