Dynamical Systems Magazine
July, 2004
Mathematical interaction between the richer and developing countries.
July, 2004
Mathematical interaction between the richer and developing countries.
April, 2004
SIAG/DS 2004 election results
January, 2004
Jack K. Hale in the spotlight
October, 2003
Industrial (or industrious?) experience: What is DSWeb?
May, 2003
Launch of DSWeb Magazine

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, Urbana-Champaign 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 8-13). 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 Saddle-Node and Pitchfork bifurcations, Lorentz , and Bogdanov-Takens 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.

Book Reviews
Computational Homology -- July, 2004
Stability and Oscillations of Nonlinear Pulse-Modulated Systems -- July, 2004
The Dynamics of Control -- July, 2004
Books in Brief -- July, 2004
An Introduction to Dynamical Systems: Continuous and Discrete -- April, 2004
Vibrational Mechanics: Nonlinear Dynamic Effects, General Approach, Applications -- April, 2004
Nonlinear Analysis and its Application to Differential Equations -- April, 2004
Books in brief -- April, 2004
Books in brief -- January, 2004
Methods in Equivariant Bifurcations and Dynamical Systems -- January, 2004
Changing Mind, Transitions in Natural and Artificial Environments -- January, 2004
Order and Chaos in Dynamical Astronomy -- January, 2004
Nonlinear Dynamics and Chaos: Where do we go from here -- October, 2003
Normal Forms and Unfoldings for Local Dynamical Systems -- October, 2003
Books in brief -- October, 2003
Interesting reprints -- October, 2003
New applications of nonlinear and chaotic dynamics in mechanics -- October, 2003
Global Analysis of Dynamical Systems -- May, 2003
Interesting reprints -- May, 2003
Nonlinear Dynamics of Interacting Populations -- May, 2003
Linear and Nonlinear Rotor Dynamics -- May, 2003
Dynamical Systems with Applications using Maple &
Nonlinear Physics with Maple or Mathematica for Scientists and Engineers -- May, 2003
Books in brief -- May, 2003