Overview

The present book is a translation and an expansion of lecture notes cor- sponding to a course of Mathematics of Control delivered during four years at the Ecole Nationale des Ponts et Chauss ees (Marne-la-Vall ee, France) to Master students. A reduced version of this course has also been given at the Master level at the University of Paris-Sud since eight years. It may the- fore serve as lecture notes for teaching at the Master or PhD level but also as a comprehensive introduction to researchers interested in atness and more generally in the mathematical theory of nite dimensional systems and c- trol. This book may be seen as an outcome of the applied research policy pi- oneered by the Ecole des Mines de Paris (now MINES-ParisTech), France, aiming not only at academic excellence, but also at collaborating with - dustries on speci c innovative projects to enhance technological innovation using the most advanced know-how. This in uence, though indirectly visible, mainly concerns the originality of some of the topics addressed here which are, in a sense, a theoretic synthesis of the author's applied contributions and viewpoints in the control eld, continuously elaborated and modi ed in contact with the industrial realities. Such a synthesis wouldn't have been made possible without the scienti c trust and nancial support of many c- panies during periods ranging from two to ten years.

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From the reviews: This book is focused mainly on the analysis of so-called nonlinear flat systems. ! The book is published in the mathematical engineering series, and as a consequence the differential geometry content is presented in a very accessible applied mathematics way. (Guy Jumarie, Zentralblatt MATH, Vol. 1167, 2009)

From the reviews: This book is focused mainly on the analysis of so-called nonlinear flat systems. ! The book is published in the mathematical engineering series, and as a consequence the differential geometry content is presented in a very accessible applied mathematics way. (Guy Jumarie, Zentralblatt MATH, Vol. 1167, 2009) This book provides an introduction to the theory of deterministic, continuous-time, finite-dimensional, nonlinear control systems from the particular 'differential-algebraic' point of view, with the notion of 'flatness' as the fundamental underlying principle. ! this book is the first extensive treatment of the notion of flatness in monograph form. As such, it is certainly a useful addition to the control-theory literature. A particular strength of the book is its detailed treatment of many examples ! . (Kevin A. Grasse, Mathematical Reviews, Issue 2011 j)

"From the reviews: ""This book is focused mainly on the analysis of so-called nonlinear flat systems. … The book is published in the mathematical engineering series, and as a consequence the differential geometry content is presented in a very accessible applied mathematics way."" (Guy Jumarie, Zentralblatt MATH, Vol. 1167, 2009) “This book provides an introduction to the theory of deterministic, continuous-time, finite-dimensional, nonlinear control systems from the particular ‘differential-algebraic’ point of view, with the notion of ‘flatness’ as the fundamental underlying principle. … this book is the first extensive treatment of the notion of flatness in monograph form. As such, it is certainly a useful addition to the control-theory literature. A particular strength of the book is its detailed treatment of many examples … .” (Kevin A. Grasse, Mathematical Reviews, Issue 2011 j)"

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