Well-posed infinite horizon variational problems on a compact manifold Export

@article{citeulike:4968023, abstract = {We give an effective sufficient condition for a variational problem with infinite horizon on a compact Riemannian manifold M to admit a smooth optimal synthesis, i. e. a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis we construct a well-projected to M invariant Lagrange submanifold of the extremals' flow in the cotangent bundle T*M. The construction uses the curvature of the flow in the cotangent bundle and some ideas of hyperbolic dynamics.}, archivePrefix = {arXiv}, author = {Agrachev, Andrei}, citeulike-article-id = {4968023}, citeulike-linkout-0 = {http://arxiv.org/abs/0906.4433}, citeulike-linkout-1 = {http://arxiv.org/pdf/0906.4433}, day = {24}, eprint = {0906.4433}, keywords = {dynamical\_systems, optimization\_control, riemannian\_geometry}, month = {Jun}, posted-at = {2009-06-26 07:32:11}, priority = {2}, title = {Well-posed infinite horizon variational problems on a compact manifold}, url = {http://arxiv.org/abs/0906.4433}, year = {2009} }

TY - JOUR ID - citeulike:4968023 L3 - citeulike-article-id:4968023 N2 - We give an effective sufficient condition for a variational problem with infinite horizon on a compact Riemannian manifold M to admit a smooth optimal synthesis, i. e. a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis we construct a well-projected to M invariant Lagrange submanifold of the extremals' flow in the cotangent bundle T*M. The construction uses the curvature of the flow in the cotangent bundle and some ideas of hyperbolic dynamics. TI - Well-posed infinite horizon variational problems on a compact manifold KW - dynamical_systems KW - optimization_control KW - riemannian_geometry AU - Agrachev, Andrei PY - 2009/Jun/24/ UR - http://arxiv.org/abs/0906.4433 ER -