# Optimal control on distributions

arXiv: https://arxiv.org/abs/1702.02750 · HTML: https://mlsanity.com/paper/1702.02750/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2017.

## Built on by (most cited first, 1 of 1)

- [Deep Learning Approximation of Diffeomorphisms via Linear-Control Systems](https://mlsanity.com/paper/2110.12393/) (2021)

## Abstract (arXiv)

This paper studies (single-time and multitime) optimal control problems on a nonholonomic manifold (described either by the kernel of a Gibbs-Pfaff form or by the span of appropriate vector fields). For both descriptions we analyse: infinitesimal deformations and adjointness, single-time optimal control problems, multitime optimal control problem of maximizing a multiple integral functional, multitime optimal control problem of maximizing a curvilinear integral functional, Curvilinear functionals depending on curves, optimization of mechanical work on Riemannian manifolds. Also we prove that a nonholonomic system can be always controlled by uni-temporal or bi-temporal bang-bang controls.