Geometric Control Theory

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Dezember 1996



A modern version of the calculus of variations, encompassing geometric mechanics, differential geometry, and optimal control.


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 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
EAN: 9780521495028
ISBN: 0521495024
Untertitel: 'Cambridge Studies in Advanced'. New. Sprache: Englisch.
Erscheinungsdatum: Dezember 1996
Seitenanzahl: 512 Seiten
Format: gebunden
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