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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 Minimum energy control ： ウィキペディア英語版 Minimum energy control In control theory, the minimum energy control is the control $u(t)$ that will bring a linear time invariant system to a desired state with a minimum expenditure of energy. Let the linear time invariant (LTI) system be : $\backslash dot(t)\; +\; B\; \backslash mathbf(t)$ : $\backslash mathbf(t)\; =\; C\; \backslash mathbf(t)\; +\; D\; \backslash mathbf(t)$ with initial state $x(t\_0)=x\_0$. One seeks an input $u(t)$ so that the system will be in the state $x\_1$ at time $t\_1$, and for any other input $\backslash bar(t)$, which also drives the system from $x\_0$ to $x\_1$ at time $t\_1$, the energy expenditure would be larger, i.e., :$\backslash int\_^\; \backslash bar^$ *(t) \bar(t) dt \ \geq \ \int_^ u^ *(t) u(t) dt. To choose this input, first compute the controllability gramian :$W\_c(t)=\backslash int\_^t\; e^BB^$ *e^ d\tau. Assuming $W\_c$ is nonsingular (if and only if the system is controllable), the minimum energy control is then :$u(t)\; =\; -B^$ *e^W_c^(t_1)(). Substitution into the solution :$x(t)=e^x\_0+\backslash int\_^e^Bu(\backslash tau)d\backslash tau$ verifies the achievement of state $x\_1$ at $t\_1$. ==See also== * LTI system theory * Control engineering * State space (controls) 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「Minimum energy control」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.