Geometric Control Theory
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Geometric Control Theory: (Series Number 52 Cambridge Studies in Advanced Mathematics)

Geometric Control Theory: (Series Number 52 Cambridge Studies in Advanced Mathematics)


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About the Book

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.

Table of Contents:
Introduction; Acknowledgments; Part I. Reachable Sets and Controllability: 1. Basic formalism and typical problems; 2. Orbits of families of vector fields; 3. Reachable sets of Lie-determined systems; 4. Control affine systems; 5. Linear and polynomial control systems; 6. Systems on Lie groups and homogenous spaces; Part II. Optimal Control Theory: 7. Linear systems with quadratic costs; 8. The Riccati equation and quadratic systems; 9. Singular linear quadratic problems; 10. Time-optimal problems and Fuller's phenomenon; 11. The maximum principle; 12. Optimal problems on Lie groups; 13. Symmetry, integrability and the Hamilton-Jacobi theory; 14. Integrable Hamiltonian systems on Lie groups: the elastic problem, its non-Euclidean analogues and the rolling-sphere problem; References; Index.

Review :
Review of the hardback: '… should find a place on the reading lists for all graduate courses which contain this aspect of control theory.' D. J. Bell, UMIST Review of the hardback: '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 Review of the hardback: '… the book will be of interest to physicists and engineers … it should be attractive for mathematicians …'. European Mathematical Society Review of the hardback: '… 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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Product Details
  • ISBN-13: 9780521058247
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Height: 230 mm
  • No of Pages: 512
  • Returnable: N
  • Series Title: Series Number 52 Cambridge Studies in Advanced Mathematics
  • Weight: 793 gr
  • ISBN-10: 0521058244
  • Publisher Date: 28 Jan 2008
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Returnable: N
  • Spine Width: 30 mm
  • Width: 153 mm


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