Geometric control theory
著者
書誌事項
Geometric control theory
（Cambridge studies in advanced mathematics, 52）
Cambridge University Press, 2008, c1997
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注記
"First published 1997. This digitally printed version 2008"--T.p. verso
"Paperback re-issue"--Back cover
Includes bibliographical references (p. 483-487) and index
内容説明・目次
内容説明
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.
目次
- 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.
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