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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 Algebraic Riccati equation ： ウィキペディア英語版 Algebraic Riccati equation An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time or discrete time. A typical algebraic Riccati equation is similar to one of the following: the continuous time algebraic Riccati equation (CARE): : $A^T\; X\; +\; X\; A\; -\; X\; B\; R^\; B^T\; X\; +\; Q\; =\; 0\; \backslash ,$ or the discrete time algebraic Riccati equation (DARE): : $X\; =\; A^T\; X\; A\; -(A^T\; X\; B)(R\; +\; B^T\; X\; B)^(B^T\; X\; A)\; +\; Q.\backslash ,$ ''X'' is the unknown ''n'' by ''n'' symmetric matrix and ''A'', ''B'', ''Q'', ''R'' are known real coefficient matrices. Though generally this equation can have many solutions, it is usually specified that we want to obtain the unique stabilizing solution, if such a solution exists. ==Origin of the name== The name Riccati is given to these equations because of their relation to the Riccati differential equation. Indeed, the CARE is verified by the time invariant solutions of the associated matrix valued Riccati differential equation. As fore the DARE, it is verified by the time invariant solutions of the matrix valued Riccati difference equation (which is the analogue of the Riccati differential equation in the context of discrete time LQR). 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「Algebraic Riccati equation」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.