On Controllability of Driftless Control System on Symmetric Spaces

TL;DR

This paper investigates the controllability of driftless control systems on symmetric spaces, providing conditions for global controllability and illustrating with examples from SE(3) and random matrix ensembles.

Contribution

It establishes new global controllability conditions for driftless systems on symmetric spaces, expanding understanding in geometric control theory.

Findings

Global controllability condition derived for symmetric spaces

Examples include exponential submanifolds of SE(3)

Applications to random matrix ensembles

Abstract

Symmetric spaces arise in wide variety of problems in Mathematics and Physics. They are mostly studied in Representation theory, Harmonic analysis and Differential geometry. As many physical systems have symmetric spaces as their configuration spaces, the study of controllability on symmetric space is quite interesting. In this paper, a driftless control system of type \dot{x}= \sum_{i=1}^m u_if_i(x) is considered on a symmetric space. For this we have established global controllability condition which is illustrated by few examples of exponential submanifolds of SE(3) and random matrix ensembles.