Towards funnel control on Riemannian manifolds

Funnel control for time-invariant control-affine systems with relative degree one is transferred to the case of dynamical systems evolving on a Riemannian manifold. It is shown that, under some regularity assumptions, the classical proofs carry over. The regularity assumptions reflect the particularities of the nonlinear theory and degenerate in the classical Euclidean case.