  For a right-invariant system on a compact Lie group G, I present two methods
to design a control to drive the state from the identity to any element of the
group. The first method, under appropriate assumptions, achieves exact control
to the target but requires estimation of the `size' of a neighborhood of the
identity in G. The second method, does not involve any mathematical difficulty,
and obtains control to a desired target with arbitrary accuracy. A third method
is then given combining the main ideas of the previous methods. This is also
very simple in its formulation and turns out to be generically more efficient
as illustrated by one of the examples we consider.
  The methods described in the paper provide arbitrary constructive control for
any right-invariant system on a compact Lie group. I give examples including
closed multilevel quantum systems and lossless electrical networks. In
particular, the results can be applied to the coherent control of general
multilevel quantum systems.
