Geometry of Optimal Control for Control-Affine Systems

Symmetry Integrability and Geometry-Methods and Applications

article

Jeanne N. Clelland¹  Christopher G. Moseley²  George R. Wilkens³ 

[1] Department of Mathematics, University of Colorado;Department of Mathematics and Statistics, Calvin College;Department of Mathematics, University of Hawaii at Manoa

关键词: af fine distributions;    optimal control theory;    Cartan’s method of equivalence;   

DOI  :  10.3842/SIGMA.2013.034

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown