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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Control Theory from the Geometric Viewpoint

Control Theory from the Geometric Viewpoint

Agrachev, Andrei A.
Sachkov, Yuri

Hardcover

Series: Encyclopaedia of Mathematical Sciences, Book 87

General MathematicsGeneral Science

ISBN10: 3540210199
ISBN13: 9783540210191
Publisher: Springer Nature
Published: Apr 15 2004
Pages: 412
Weight: 1.71
Height: 0.94 Width: 6.14 Depth: 9.21
Language: English
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.

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