Geometric Control Theory

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Paperback | 28 January 2008

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512 Pages

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22.86 x 15.24 x 2.9

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Geometric control theory is concerned with the evolution of systems subject to physical laws but having some degree of freedom through which motion is to be controlled. This book describes the mathematical theory inspired by the irreversible nature of time evolving events. The first part of the book deals with the issue of being able to steer the system from any point of departure to any desired destination. The second part deals with optimal control, the question of finding the best possible course. An overlap with mathematical physics is demonstrated by the Maximum principle, a fundamental principle of optimality arising from geometric control, which is applied to time-evolving systems governed by physics as well as to man-made systems governed by controls. Applications are drawn from geometry, mechanics, and control of dynamical systems. The geometric language in which the results are expressed allows clear visual interpretations and makes the book accessible to physicists and engineers as well as to mathematicians.

Industry Reviews

From the hardback review: '... should find a place on the reading lists for all graduate courses which contain this aspect of control theory.' D. J. Bell, Department of Mathematics, UMIST From the hardback review: 'Without doubt the book is extremely well written, and the intrinsically geometric nature of the language through which fundamental concepts are expressed lends itself to the clear visual representations which will appeal to scientists and engineers.' Peter Larcombe, Mathematics Today From the hardback review: '... the book will be of interest to physicists and engineers ... it should be attractive for mathematicians ...'. European Mathematical Society From the hardback review: '... an important reference for graduate students and mathematicians ... well written, almost self-contained, and easy to read.' M. F. Silva Leite, Zentralblatt MATH

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Introduction
Acknowledgments
Reachable Sets and Controllability
Basic formalism and typical problems
Orbits of families of vector fields
Reachable sets of Lie-determined systems
Control affine systems
Linear and polynomial control systems
Systems on Lie groups and homogenous spaces
Optimal Control Theory
Linear systems with quadratic costs
The Riccati equation and quadratic systems
Singular linear quadratic problems
Time-optimal problems and Fuller's phenomenon
The maximum principle
Optimal problems on Lie groups
Symmetry, integrability and the Hamilton-Jacobi theory
Integrable Hamiltonian systems on Lie groups: the elastic problem, its non-Euclidean analogues and the rolling-sphere problem
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

Geometric Control Theory

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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