
The Dynamics of Control 

The Dynamics of Control
Fritz Colonius and Wolfgang
Kliemann, Birkhauser Press (2000), price $99, ISBN
0817636838. 
Reviewer: V. Zharnitsky, University
of Illinois, UrbanaChampaign
USA.  The Dynamics of
Control provides a non traditional approach to the
subjects of Dynamical Systems theory and Control theory.
It is probably the first book where such notions as
Morse decomposition, chain recurrence from dynamical
systems theory are systematically used for control
systems. Previous books treating dynamics and control
usually consider the two as separate subjects.
The main text consists of the three parts: Global
Theory, Linearization, and Applications. There is a
short instructive introduction and an appendix where the
necessary background can be found for virtually any
reader (chapter on dynamical systems for which might be
useful for control theorists and a chapter on geometric
control theory that will be helpful for the readers who
are less familiar with control theory). Given that the
goal is to bring together the two communities, such self
contained appendix is very helpful.
In the informal introduction eight basic problems at
the interface of dynamics and control are formulated,
which are later developed throughout the book. (The
problems are formulated somewhat implicitly. It takes
some effort to realize what they are).
The book contains many examples which are helpful in
mastering the material. There is even a special section
on applications (chapters 813). Many examples go all
the way from abstract notions to getting the actual
numbers (obtained either numerically or analytically).
For readers familiar with dynamical systems theory it
would be interesting to see such classical examples as
SaddleNode and Pitchfork bifurcations, Lorentz , and
BogdanovTakens systems presented in the context of
control systems.
In Summary, this book provides a fresh look at
classical dynamics problems and is a source of new
problems for dynamics community. Also, the systematic
use of dynamical systems theory as applied to control
systems should be interesting to control
theorists.   
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