A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Geometry of Optimal Control for Control-Affine Systems
2013
Symmetry, Integrability and Geometry: Methods and Applications
Preserved Fulltext
Other Versions
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
doi:10.3842/sigma.2013.034
fatcat:hbx2tzrk3bgspm4d2g7fsd3yam