%0 Journal Article
%T Geometry of Optimal Control for Control-Affine Systems
%A Jeanne N. Clelland
%A Christopher G. Moseley
%A George R. Wilkens
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2013
%I National Academy of Science of Ukraine
%R 10.3842/sigma.2013.034
%X 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.
%K affine distributions
%K optimal control theory
%K Cartan's method of equivalence
%U http://dx.doi.org/10.3842/SIGMA.2013.034