The General Solution for Affine Control Systems on Lie Groups

Abstract

The purpose of this paper is to present explicitly the solution curve for affine control systems on Lie groups under the assumption that automorphisms associated to the linear vector fields commutes. If we assume that the derivations associated to linear vector fields are inner, we obtain a simpler solution and we show some results of controllability. To end, we work with conjugation by homomorphism of Lie groups between affine systems.