Optimal control and geometry : integrable systems / Velimir Jurdjevic, University of Toronto.
The synthesis of symplectic geometry, the calculus of variations and control theory offered in this book provides a crucial foundation for the understanding of many problems in applied mathematics. Focusing on the theory of integrable systems, this book introduces a class of optimal control problems...
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Full Text (via Cambridge) |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge, United Kingdom :
Cambridge University Press,
2016.
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| Series: | Cambridge studies in advanced mathematics ;
154. |
| Subjects: |
Table of Contents:
- The Orbit theorem and Lie determined systems
- Control systems: accessibility and controllability
- Lie groups and homogeneous spaces
- Symplectic manifolds: Hamiltonian vector fields
- Poisson manifolds, Lie algebras, and coadjoint orbits
- Hamiltonians and optimality: the Maximum Principle
- Hamiltonian view of classic geometry
- Symmetric spaces and sub-Riemannian problems
- Affine-quadratic problem
- Contangent bundles of homogeneous spaces as coadjoint orbits
- Elliptic geodesic problem on the sphere
- Rigid body and its generalizations
- Isometry groups of space forms and affine systems: Kirchoff's elastic problem
- Kowalewski-Lyapunov criteria
- Kirchhoff-Kowalewski equation
- Elastic problems on symmetric spaces: the Delauney-Dubins problem
- The non-linear Schroedinger's equation and Heisenberg's magnetic equation-solitons.