Document Type
Article
Publication Title
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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.
DOI
10.3842/SIGMA.2013.034
Publication Date
8-26-2013
Recommended Citation
Clelland, Jeanne N.; Moseley, Christopher G.; and Wilkens, George R., "Geometry of optimal control for control-affine systems" (2013). University Faculty Publications and Creative Works. 281.
https://digitalcommons.calvin.edu/calvin_facultypubs/281