Geometric Control Theory
Geometric Control Theory
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
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
Product details
January 2008Paperback
9780521058247
512 pages
230 × 153 × 30 mm
0.821kg
81 b/w illus.
Available
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.
