<電子ブック>
Control Theory from the Geometric Viewpoint / by Andrei A. Agrachev, Yuri Sachkov
(Encyclopaedia of Mathematical Sciences ; 87)
版 | 1st ed. 2004. |
---|---|
出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
出版年 | 2004 |
本文言語 | 英語 |
大きさ | XIV, 412 p : online resource |
著者標目 | *Agrachev, Andrei A author Sachkov, Yuri author SpringerLink (Online service) |
件 名 | LCSH:System theory LCSH:Control theory FREE:Systems Theory, Control |
一般注記 | 1 Vector Fields and Control Systems on Smooth Manifolds -- 2 Elements of Chronological Calculus -- 3 Linear Systems -- 4 State Linearizability of Nonlinear Systems -- 5 The Orbit Theorem and its Applications -- 6 Rotations of the Rigid Body -- 7 Control of Configurations -- 8 Attainable Sets -- 9 Feedback and State Equivalence of Control Systems -- 10 Optimal Control Problem -- 11 Elements of Exterior Calculus and Symplectic Geometry -- 12 Pontryagin Maximum Principle -- 13 Examples of Optimal Control Problems -- 14 Hamiltonian Systems with Convex Hamiltonians -- 15 Linear Time-Optimal Problem -- 16 Linear-Quadratic Problem -- 17 Sufficient Optimality Conditions, Hamilton-Jacobi Equation, and Dynamic Programming -- 18 Hamiltonian Systems for Geometric Optimal Control Problems -- 19 Examples of Optimal Control Problems on Compact Lie Groups -- 20 Second Order Optimality Conditions -- 21 Jacobi Equation -- 22 Reduction -- 23 Curvature -- 24 Rolling Bodies -- A Appendix -- A.2 Remainder Term of the Chronological Exponential -- References -- List of Figures This book presents some facts and methods of the Mathematical Control Theory treated from the geometric point of view. The book is mainly based on graduate courses given by the first coauthor in the years 2000-2001 at the International School for Advanced Studies, Trieste, Italy. Mathematical prerequisites are reduced to standard courses of Analysis and Linear Algebra plus some basic Real and Functional Analysis. No preliminary knowledge of Control Theory or Differential Geometry is required. What this book is about? The classical deterministic physical world is described by smooth dynamical systems: the future in such a system is com pletely determined by the initial conditions. Moreover, the near future changes smoothly with the initial data. If we leave room for "free will" in this fatalistic world, then we come to control systems. We do so by allowing certain param eters of the dynamical system to change freely at every instant of time. That is what we routinely do in real life with our body, car, cooker, as well as with aircraft, technological processes etc. We try to control all these dynamical systems! Smooth dynamical systems are governed by differential equations. In this book we deal only with finite dimensional systems: they are governed by ordi nary differential equations on finite dimensional smooth manifolds. A control system for us is thus a family of ordinary differential equations. The family is parametrized by control parameters HTTP:URL=https://doi.org/10.1007/978-3-662-06404-7 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
|
Springer eBooks | 9783662064047 |
|
電子リソース |
|
EB00233878 |
書誌詳細を非表示
データ種別 | 電子ブック |
---|---|
分 類 | LCC:Q295 LCC:QA402.3-402.37 DC23:003 |
書誌ID | 4000110689 |
ISBN | 9783662064047 |
類似資料
この資料の利用統計
このページへのアクセス回数:4回
※2017年9月4日以降