EAN: 9783540210191

CONTROL THEORY FROM THE GEOMETRIC VIEWPOINT - A...

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.

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