  We study the Hopf algebra H of Fliess operators coming from Control Theory in
the one-dimensional case. We prove that it admits a graded, finte-dimensional,
connected gradation. Dually, the vector space IR is both a pre-Lie algebra for
the pre-Lie product dual of the coproduct of H, and an associative, commutative
algebra for the shuffle product. These two structures admit a compatibility
which makes IR a Com-pre-Lie algebra. We give a presentation of this object as
a Com-pre-Lie algebra and as a pre-Lie algebra.
