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.
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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