Geometry of Optimal Control for Control-Affine Systems

被引：3
|
作者：
Clelland, Jeanne N. [1 ]
Moseley, Christopher G. [2 ]
Wilkens, George R. [3 ]
机构：
[1] Univ Colorado, Dept Math, Boulder, CO 80309 USA
[2] Calvin Coll, Dept Math & Stat, Grand Rapids, MI 49546 USA
[3] Univ Hawaii Manoa, Dept Math, Honolulu, HI 96822 USA
来源：
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2013年 / 9卷
关键词：
affine distributions; optimal control theory; Cartan's method of equivalence;
D O I：
10.3842/SIGMA.2013.034
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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.
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页数：31
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