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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 Legendre–Clebsch condition ： ウィキペディア英語版 Legendre–Clebsch condition In the calculus of variations the Legendre–Clebsch condition is a second-order condition which a solution of the Euler–Lagrange equation must satisfy in order to be a maximum (and not a minimum or another kind of extremal). For the problem of maximizing :$\backslash int\_^\; L(t,x,x\text{'})\backslash ,\; dt\; .\; \backslash ,$ the condition is :$0\; \backslash ge\; L\_(t,x(t),x\text{'}(t)),\; \backslash ,\; \backslash forall\; t\; \backslash in()$ ==Generalized Legendre-Clebsch== In optimal control, the situation is more complicated because of the possibility of a singular solution. The generalized Legendre–Clebsch condition,〔H.M. Robbins, A generalized Legendre-Clebsch condition for the singular cases of optimal control, IBM Journal of Research and Development, 1967〕 also known as convexity, is a sufficient condition for local optimality such that when the linear sensitivity of the Hamiltonian to changes in u is zero, i.e., : $\backslash frac\; =\; 0$ The Hessian of the Hamiltonian is positive definite along the trajectory of the solution: : $\backslash frac\; >\; 0$ In words, the generalized LC condition guarantees that over a singular arc, the Hamiltonian is minimized. 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「Legendre–Clebsch condition」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.