Here is the listing of Best reference books on Differential Geometric Methods in Control.
|1. “Ordinary Differential Equations” by V. Arnold
Book Review: This book is very useful for graduate and undergraduate students studying the qualitative theory of ordinary differential equations. The book contains chapters on vector field, phase space, phase flow, one parameter transformation groups and many more. All the ideas are expressions with easy notations, minimum formalism and good motivation. The book contains numerous examples, problems and figures. The book demonstrates many applications that are taken mainly from mechanics. The book also stresses on geometrical aspects along with flows, manifolds and tangent bundles.
|2. “A Comprehensive Introduce to Differential Geometry” by M. Spivak|
|3. “Nonlinear Control Systems” by A. Isidori
Book Review: This book presents the fundamentals of the theory of nonlinear control systems thereby stressing on differential geometric approach. This is a very good graduate level textbook as well as a very good reference book for scientists and researchers who are dealing with the analysis and design of feedback systems. The information in the book is the result of author’s experience gained at various universities. The book contains chapters at a more elementary level.
|4. “Introduction to Mechanics and Symmetry” by J. Marsden and T Ratiu
Book Review: This book deals with the development of basic theory and application of mechanics thereby stressing on the role of symmetry. The book also includes various applications thereby making it very useful to physicists and engineers. The book also provides many examples and applications that demonstrate the working of theory thereby making it very useful for readers and graduates and undergraduates studying mathematics, physics and engineering. The book also contains many exercises which are successful in testing the understanding of the user.
|5. “Control Theory from the Geometric Viewpoint” by A Agrachev and Y. Sachkov
Book Review: The book demonstrates various facts and methods that are related to mathematical control theory. All the facts and methods are illustrated from geometric point of view. The prerequisites to this book are analysis courses and linear algebra along with some basic real and functional analysis. The book does not require prior knowledge of control theory or differential geometry. The book very nicely describes dynamical systems which are the systems determined by initial conditions. This book deals with finite dimensional systems only.
Sanfoundry Global Education & Learning Series – Best Reference Books!