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.
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)