Continuity of reachable sets of restricted affine control systems

TL;DR

This paper proves that the reachable sets of restricted affine control systems on connected manifolds change continuously over time when measured with the Hausdorff metric, ensuring stability of control reachability.

Contribution

It provides a direct proof of the continuity of reachable sets for restricted affine control systems on connected manifolds, a result previously not explicitly established.

Findings

Reachable sets vary continuously with time

Continuity is measured using the Hausdorff metric

Applicable to restricted affine control systems on connected manifolds

Abstract

In this paper we give a direct proof that for a restricted affine control system on a connected manilfold M, the associated reachable sets up to time t varies continuously with the Haudorff metric.