Optimal Control and Geometry: Integrable Systems

Professor Velimir Jurdjevic is one of the founders of geometric control theory. His pioneering work with H. J. Sussmann was deemed to be among the most influential papers of the century and his book, Geometric Control Theory, revealed the geometric origins of the subject and uncovered important connections to physics and geometry. It remains a major reference on non-linear control. Jurdjevic's expertise also extends to differential geometry, mechanics and integrable systems. His publications cover a wide range of topics including stability theory, Hamiltonian systems on Lie groups, and integrable systems. He has spent most of his professional career at the University of Toronto.

• 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.

'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