Geometry of control-affine systems

Authors

Jeanne N. Clelland, University of Colorado BoulderFollow
Christopher G. Moseley, Calvin UniversityFollow
George R. Wilkens, University of Hawaiʻi at MānoaFollow

Document Type

Article

Publication Title

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Abstract

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.

DOI

10.3842/SIGMA.2009.095

Publication Date

12-1-2009

Recommended Citation

Clelland, Jeanne N.; Moseley, Christopher G.; and Wilkens, George R., "Geometry of control-affine systems" (2009). University Faculty Publications and Creative Works. 280.
https://digitalcommons.calvin.edu/calvin_facultypubs/280