Control Theory from the Geometric Viewpoint 2004th Edition by Andrei A. Agrachev (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review Aus den Rezensionen:”Der Band ist aus Graduiertenkursen an der International School for Advanced Studies in Triest entstanden … Mathematisch werden gute Kenntnisse der Analysis, der linearen Algebra und der Funktionalanalysis vorausgesetzt. … Bekannte und neue Beispiele … illustrieren hier die Fülle an Aussagen in sehr anschaulicher Weise. Insgesamt ist so ein Band entstanden, der Mathematikern und mathematisch interessierten Anwendern wertvolle Anregungen bei der Auseinandersetzung mit gesteuerten bzw. geregelten nichtlinearen Systemen und deren Optimierung bietet.”(l. Troch, in: IMN – Internationale Mathematische Nachrichten, 2006, Issue 202, S. 44 f.) About the Author Andrei A. AgrachevBorn 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, Italyand Leading Researcher of the Steklov Ins. for Math., Moscow, Russia Yuri L. SachkovBorn 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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a beautiful introduction to the subject.The authors gave a very personal touch to the subject, and have enriched the book with their well reputable wisdom in the subject.Wit comments abound everywhere (e.g. see preface, where controlled dynamical systems are compared to the assumption of free will), and instead a full blown over-generalized exposition they appeal instead to digestible but insightful bites of the theory.Since I’m not acquainted with the previous reviewer level of expertise in the subject, it’s hard to figure out his personal reasons for an irate attack to the notation in the present book.If truth be said, this is a book for a well-educated gentleman or madam in the arts of mathematical sciences — way beyond perhaps a more utilitarian introduction based on Matlab for example. This includes not only mathematicians, but physicists and control engineers too concerned about foundational aspect of their subject matter.Last but not least permit me to appraise briefly some examples contained herein.Agrachev et al.’s book is one of the few treatises dealing with rolling problems, a classic problem in nonholonomic control.Optimal control is also gracefully illustrated too. See for example a worked exercise on the fastest stop of a passenger train, or optimal control of a rigid body. (Engineers interested in attitude control may consider have a quick glance at a more mathematical formulation of the problem.)Not to appeal to academic authority, but both authors descend from Pontryagin’s control school in Moscow. In fact the senior author Agrached is an academic grandson of Pontryagin himself, and therefore I’d like to view this book as a near first-account explanation of inner workings of the maximum principle.It is unfortunate that the previous reviewer had to in a harsh manner misjudge such superb book based only on notational strength.

⭐This book is not well-written. It does not use standard notation but defines its own notation, which is very confusing. For nonlinear control theory, I would recommend “Geometric Control of Mechanical Systems: Modeling, Analysis, and Design for Simple Mechanical Control Systems” by Bullo and Lewis.

⭐

⭐

⭐

Keywords

Free Download Control Theory from the Geometric Viewpoint 2004th Edition in PDF format
Control Theory from the Geometric Viewpoint 2004th Edition PDF Free Download
Download Control Theory from the Geometric Viewpoint 2004th Edition 2004 PDF Free
Control Theory from the Geometric Viewpoint 2004th Edition 2004 PDF Free Download
Download Control Theory from the Geometric Viewpoint 2004th Edition PDF
Free Download Ebook Control Theory from the Geometric Viewpoint 2004th Edition