Control Theory from the Geometric Viewpoint
Control Theory from the Geometric Viewpoint
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DOI：
10.1007/978-3-662-06404-7
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发表时间：
2004-04
期刊：
影响因子：
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通讯作者：
A. Agrachev;Y. Sachkov
中科院分区：
文献类型：
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作者：
A. Agrachev;Y. Sachkov
本书介绍了从几何角度处理的数学控制理论的一些事实和方法。本书主要基于第一合著者2000-2001年在意大利的里雅斯特国际高级研究学院教授的研究生课程。数学先决条件减少为分析和线性代数的标准课程以及一些基本的实数和泛函分析。不需要控制理论或微分几何的初步知识。这本书是关于什么的？经典的确定性物理世界是由平滑的动力系统描述的：这种系统的未来完全由初始条件决定。而且，近期的数据与初始数据的变化也很顺利。如果我们在这个宿命论的世界中留有“自由意志”的空间，那么我们就会控制系统。我们通过允许动力系统的某些参数在每个时刻自由变化来实现这一点。这就是我们在现实生活中经常对我们的身体、汽车、炊具以及飞机、技术流程等所做的事情。我们试图控制所有这些动力系统！光滑动力系统由微分方程控制。在本书中，我们只处理有限维系统：它们由有限维光滑流形上的常微分方程控制。因此，我们的控制系统是一组常微分方程。该族由控制参数参数化。
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.