Geometric reduction in optimal control theory with symmetries

A general study of symmetries in optimal control theory is given, starting from the presymplectic description of this kind of system. Then, Noether's theorem, as well as the corresponding reduction procedure (based on the application of the Marsden-Weinstein theorem adapted to the presymplectic case) are stated both in the regular and singular cases, which are previously described.Comment: 24 pages. LaTeX file. The paper has been reorganized. Additional comments have been included in Section 3. The example in Section 5.2 has been revisited. Some references have been adde

Orbit Theorems and Sampling

This paper proposes a notion of smooth action on a manifold, and establishes a general integrability result for certain associated distributions. As corollaries, various classical and new results on manifold structures of orbits are established, and the main theorem on preservation of transitivity under sampling is shown to be a simple consequence