Encyclopaedia of Mathematical Sciences

Control Theory from the Geometric Viewpoint

Authors: Agrachev, Andrei A., Sachkov, Yuri

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About this book

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.

About the authors

Andrei A. Agrachev

Born in Moscow, Russia.

Graduated: Moscow State Univ., Applied Math. Dept., 1974.

Ph.D.: Moscow State Univ., 1977.

Doctor of Sciences (habilitation): Steklov Inst. for Mathematics, Moscow, 1989.

Invited speaker at the International Congress of Mathematicians ICM-94 in Zurich.

Over 90 research papers on Control Theory, Optimization, Geometry (featured review of Amer. Math. Soc., 2002).

Professional Activity: Inst. for Scientific Information, Russian Academy of Sciences, Moscow, 1977-1992; Moscow State Univ., 1989-1997; Steklov Inst. for Mathematics, Moscow, 1992-present; International School for Advanced Studies (SISSA-ISAS), Trieste, 2000-present.

Current positions: Professor of SISSA-ISAS, Trieste, Italy

and Leading Researcher of the Steklov Ins. for Math., Moscow, Russia

 

Yuri L. Sachkov

Born in Dniepropetrovsk, Ukraine.

Graduated: Moscow State Univ., Math. Dept., 1986.

Ph.D.: Moscow State Univ., 1992.

Over 20 research papers on Control Theory.

Professional Activity: Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalessky, 1989-present;

University of Pereslavl, 1993-present.

Steklov Inst. for Mathematics, Moscow, 1998-1999;

International School for Advanced Studies (SISSA-ISAS), Trieste, 1999-2001.

Current positions: Senior researcher of Program Systems Institute, Pereslavl-Zalessky, Russia;

Associate professor of University of Pereslavl, Russia.

Table of contents (24 chapters)

  • Vector Fields and Control Systems on Smooth Manifolds

    Agrachev, Andrei A. (et al.)

    Pages 1-19

    Preview Buy Chapter 30,19 €
  • Elements of Chronological Calculus

    Agrachev, Andrei A. (et al.)

    Pages 21-45

    Preview Buy Chapter 30,19 €
  • Linear Systems

    Agrachev, Andrei A. (et al.)

    Pages 47-51

    Preview Buy Chapter 30,19 €
  • State Linearizability of Nonlinear Systems

    Agrachev, Andrei A. (et al.)

    Pages 53-62

    Preview Buy Chapter 30,19 €
  • The Orbit Theorem and its Applications

    Agrachev, Andrei A. (et al.)

    Pages 63-80

    Preview Buy Chapter 30,19 €

Buy this book

eBook 130,89 €
price for Spain (gross)
  • ISBN 978-3-662-06404-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 171,59 €
price for Spain (gross)
  • ISBN 978-3-540-21019-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 171,59 €
price for Spain (gross)
  • ISBN 978-3-642-05907-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Control Theory from the Geometric Viewpoint
Authors
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
87
Copyright
2004
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-06404-7
DOI
10.1007/978-3-662-06404-7
Hardcover ISBN
978-3-540-21019-1
Softcover ISBN
978-3-642-05907-0
Series ISSN
0938-0396
Edition Number
1
Number of Pages
XIV, 412
Topics