Control Theory from the Geometric Viewpoint
Agrachev, Andrei A.; Sachkov, Yuri
ISBN 10: 3642059074 ISBN 13: 9783642059070
Editorial: Springer, 2010
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Descripción
Descripción:
N° de ref. del artículo 11862746-n
Sinopsis:
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.
Acerca del autor: 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.
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Detalles bibliográficos
Título: Control Theory from the Geometric Viewpoint
Editorial: Springer
Año de publicación: 2010
Encuadernación: Encuadernación de tapa blanda
Condición: New