Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Algebraic Geometry
Geometry Of Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens
Geometry Of Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens
University Faculty Publications and Creative Works
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 …
Geometry Of Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens
Geometry Of Control-Affine Systems, Jeanne N. Clelland, Christopher G. Moseley, George R. Wilkens
University Faculty Publications and Creative Works
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 …