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Geometric Control Theory


Part of Cambridge Studies in Advanced Mathematics

  • Date Published: May 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521058247

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About the Authors
  • 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.

    • Gives a clear conceptual grasp of practical engineering problems and the associated mathematics
    • Geometric descriptions make the subject accessible to a wide mathematical audience
    • Contains important new results on optimality in the classical calculus of variations
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    Reviews & endorsements

    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

    • Date Published: May 2008
    • format: Paperback
    • isbn: 9780521058247
    • length: 512 pages
    • dimensions: 230 x 153 x 30 mm
    • weight: 0.821kg
    • contains: 81 b/w illus.
    • availability: Available
  • Table of Contents

    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

  • Author

    Velimir Jurdjevic, University of Toronto

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