Geometry of Optimal Control for Control-Affine Systems
Differential Geometry
2013-04-18 v2 Optimization and Control
Abstract
Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for point-affine distributions of constant type with metric structures for systems with 2 states and 1 control and systems with 3 states and 1 control, and use Pontryagin's maximum principle to find geodesic trajectories for homogeneous examples. Even in these low dimensions, the behavior of these systems is surprisingly rich and varied.
Cite
@article{arxiv.1206.1101,
title = {Geometry of Optimal Control for Control-Affine Systems},
author = {Jeanne N. Clelland and Christopher G. Moseley and George R. Wilkens},
journal= {arXiv preprint arXiv:1206.1101},
year = {2013}
}