Dependence of vector fields and singular controls

TL;DR

This paper demonstrates the importance of the dependence locus in geometric control theory, highlighting how non-trivial singular trajectories often appear within it, which has implications for understanding control systems.

Contribution

It provides an example illustrating the significance of the dependence locus and the generic emergence of singular trajectories within it in control systems.

Findings

Dependence locus plays a crucial role in control theory.

Non-trivial singular trajectories are generically embedded in the dependence locus.

The example underscores the geometric significance of these phenomena.

Abstract

We show an example providing a significance in geometric control theory of the existence of the dependence locus of a system of vector fields in particular, the generic appearance of non-trivial singular trajectories embedded in the dependence locus.