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Geometric Control Theory

$86.99 (C)

Part of Cambridge Studies in Advanced Mathematics

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

$ 86.99 (C)

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About the Authors
  • This book describes the mathematical theory inspired by the irreversible nature of time-evolving events. The first part of the book deals with the ability to steer a system from any point of departure to any desired destination. The second part deals with optimal control--the problem of finding the best possible course. The author demonstrates an overlap with mathematical physics using the maximum principle, a fundamental concept 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. He draws applications from geometry, mechanics, and control of dynamical systems. The geometric language in which the author expresses the results 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

    "...remarkably well-written...I strongly recommend GCT for the use of teachers and graduate students of control theory, mechanics and mathematics (especially dynamical systems and differential geometry), as well as for the mathematician new to control theory. It is a helpful guide for anyone engaged in research or applications of optimal control." IEEE Transactions on Automatic Control

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    Product details

    • Date Published: January 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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