Affine and bilinear systems on Lie groups

TL;DR

This paper explores affine and bilinear control systems on Lie groups, revealing their intrinsic connection and analyzing controllability conditions, especially highlighting limitations on bilinear systems' controllability.

Contribution

It establishes a fundamental link between affine and bilinear systems on Lie groups and provides initial controllability results, emphasizing the restrictive nature of bilinear systems.

Findings

Controllability of affine systems on compact and solvable Lie groups.

Bilinear systems are controllable only on Euclidean spaces.

Intrinsic connection between solutions of affine and bilinear systems.

Abstract

In this paper we study affine and bilinear systems on Lie groups. We show that there is an intrinsic connection between the solutions of both systems. Such relation allows us to obtain some preliminary controllability results of affne systems on compact and solvable Lie groups. We also show that the controllability property of bilinear systems is very restricted and may only be achieved if the state space G is an Euclidean space.