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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 Backstepping ： ウィキペディア英語版 Backstepping In control theory, backstepping is a technique developed circa 1990 by Petar V. Kokotovic and others for designing stabilizing controls for a special class of nonlinear dynamical systems. These systems are built from subsystems that radiate out from an irreducible subsystem that can be stabilized using some other method. Because of this recursive structure, the designer can start the design process at the known-stable system and "back out" new controllers that progressively stabilize each outer subsystem. The process terminates when the final external control is reached. Hence, this process is known as ''backstepping.'' ==Backstepping approach== The backstepping approach provides a recursive method for stabilizing the origin of a system in strict-feedback form. That is, consider a system of the form〔 :$\backslash begin\; \backslash dot)\; +\; g\_x(\backslash mathbf)\; z\_1\backslash \backslash$ \dot_1 = f_1(\mathbf,z_1) + g_1(\mathbf,z_1) z_2\\ \dot_2 = f_2(\mathbf,z_1,z_2) + g_2(\mathbf,z_1,z_2) z_3\\ \vdots\\ \dot_i = f_i(\mathbf,z_1, z_2, \ldots, z_, z_i) + g_i(\mathbf,z_1, z_2, \ldots, z_, z_i) z_ \quad \text 1 \leq i < k-1\\ \vdots\\ \dot_ = f_(\mathbf,z_1, z_2, \ldots, z_) + g_(\mathbf,z_1, z_2, \ldots, z_) z_k\\ \dot_k = f_k(\mathbf,z_1, z_2, \ldots, z_, z_k) + g_k(\mathbf,z_1, z_2, \dots, z_, z_k) u\end where * $\backslash mathbf\; \backslash in\; \backslash mathbb^n$ with $n\; \backslash geq\; 1$, * $z\_1,\; z\_2,\; \backslash ldots,\; z\_i,\; \backslash ldots,\; z\_,\; z\_k$ are scalars, * $u$ is a scalar input to the system, * $f\_x,\; f\_1,\; f\_2,\; \backslash ldots,\; f\_i,\; \backslash ldots,\; f\_,\; f\_k$ vanish at the origin (i.e., $f\_i(0,0,\backslash dots,0)\; =\; 0$), * $g\_1,\; g\_2,\; \backslash ldots,\; g\_i,\; \backslash ldots,\; g\_,\; g\_k$ are nonzero over the domain of interest (i.e., $g\_i(\backslash mathbf,z\_1,\backslash ldots,z\_k)\; \backslash neq\; 0$ for $1\; \backslash leq\; i\; \backslash leq\; k$). Also assume that the subsystem :$\backslash dot)\; +\; g\_x(\backslash mathbf)\; u\_x(\backslash mathbf)$ is stabilized to the origin (i.e., $\backslash mathbf\; =\; \backslash mathbf\backslash ,$) by some known control $u\_x(\backslash mathbf)$ such that $u\_x(\backslash mathbf)\; =\; 0$. It is also assumed that a Lyapunov function $V\_x$ for this stable subsystem is known. That is, this $\backslash mathbf$ subsystem is stabilized by some other method and backstepping extends its stability to the $\backslash textbf$ shell around it. In systems of this ''strict-feedback form'' around a stable $\backslash mathbf$ subsystem, * The backstepping-designed control input $u$ has its most immediate stabilizing impact on state $z\_n$. * The state $z\_n$ then acts like a stabilizing control on the state $z\_$ before it. * This process continues so that each state $z\_i$ is stabilized by the ''fictitious'' "control" $z\_$. The backstepping approach determines how to stabilize the $\backslash mathbf$ subsystem using $z\_1$, and then proceeds with determining how to make the next state $z\_2$ drive $z\_1$ to the control required to stabilize $\backslash mathbf$. Hence, the process "steps backward" from $\backslash mathbf$ out of the strict-feedback form system until the ultimate control $u$ is designed. 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「Backstepping」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.