Optimal Control Theory on almost-Lie Algebroids
Optimization and Control
2011-11-08 v1 Differential Geometry
Abstract
We extend the Pontryagin Maximum Principle (PMP) to the geometric setting of almost-Lie (AL) algebroids -- objects which generalize Lie algebroids. The result may be understood as a very general reduction scheme for optimal control problems (OCPs). It covers the standard PMP, as well as gives necessary optimality conditions for symmetric OCPs on Lie groups, principal bundles, and Lie groupoids. We do not assume the symmetry of boundary conditions. The ideas are based on a very general concept of homotopy of admissible paths on AL algebroids. Our framework works for OCPs with fixed-end-points and general boundary conditions.
Cite
@article{arxiv.1111.1549,
title = {Optimal Control Theory on almost-Lie Algebroids},
author = {Michal Jozwikowski},
journal= {arXiv preprint arXiv:1111.1549},
year = {2011}
}
Comments
PhD thesis, 122 pages, with index