Optimal Control and Geometry: Integrable Systems

ISBN-13: 9781107113886 / Angielski / Twarda / 2016 / 423 str.

Velimir Jurdjevic

Opis

Blending control theory, mechanics, geometry and the calculus of variations, this book is a vital resource for graduates and researchers in engineering, mathematics and physics.

Recenzje

'The book is written in a very refreshing style that reflects the author's contagious enthusiasm for the subject. It manages this by focusing on the geometry, using the precise language of differential geometry, while not getting bogged down by analytic intricacies. Throughout, the book pays much attention to historical developments and evolving and contrasting points of view, which is also reflected in the rich bibliography of classical resources.' Matthias Kawski, MathSciNet

Spis treści

1. The orbit theorem and Lie determined systems; 2. Control systems. Accessibility and controllability; 3. Lie groups and homogeneous spaces; 4. Symplectic manifolds. Hamiltonian vector fields; 5. Poisson manifolds, Lie algebras and coadjoint orbits; 6. Hamiltonians and optimality: the Maximum Principle; 7. Hamiltonian view of classic geometry; 8. Symmetric spaces and sub-Riemannian problems; 9. Affine problems on symmetric spaces; 10. Cotangent bundles as coadjoint orbits; 11. Elliptic geodesic problem on the sphere; 12. Rigid body and its generalizations; 13. Affine Hamiltonians on space forms; 14. Kowalewski–Lyapunov criteria; 15. Kirchhoff–Kowalewski equation; 16. Elastic problems on symmetric spaces: Delauney–Dubins problem; 17. Non-linear Schroedinger's equation and Heisenberg's magnetic equation. Solitons.