Geometry of Control-Affine Systems

被引:4
|
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
关键词
affine distributions; control theory; exterior differential systems; Cartan's method of equivalence;
D O I
10.3842/SIGMA.2009.095
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X - i.e., an affine distribution F together with a distinguished vector field contained in F. We compute local invariants for point-affine distributions of constant type when dim(X) = n, rank(F) = n - 1, and when dim(X) = 3, rank(F) = 1. Unlike linear distributions, which are characterized by integer-valued invariants - namely, the rank and growth vector - when dim(X) <= 4, we find local invariants depending on arbitrary functions even for rank 1 point-affine distributions on manifolds of dimension 2.
引用
收藏
页数:28
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