Solution Curve for Linear Control Systems on Lie Groups

TL;DR

This paper explicitly derives solutions for linear control systems on Lie groups, providing formulas for specific cases and applying these to analyze controllability properties.

Contribution

It offers explicit solution formulas for linear control systems on Lie groups, especially with inner derivations, and demonstrates their use in controllability analysis.

Findings

Solutions expressed as products of exponentials for systems with inner derivations

Explicit solutions provided for low-dimensional Lie groups

Controllability results derived from the explicit solutions

Abstract

The purpose of this paper is to describe explicitly the solution for linear control systems on Lie groups. In case of linear control systems with inner derivations, the solution is given basically by the product of the exponential of the associated invariant system and the exponential of the associated invariant drift field. We present the solutions in low dimensional cases and apply the results to obtain some controllability results.