  In the context of a five-dimensional brane-world model motivated from
heterotic M-theory, we develop a framework for potential-driven brane-world
inflation. Specifically this involves a classification of the various
background solutions of (A)dS_5 type, an analysis of five-dimensional slow-roll
conditions and a study of how a transition to the flat vacuum state can be
realized. It is shown that solutions with bulk potential and both bane
potentials positive exist but are always non-separating and have a non-static
orbifold. It turns out that, for this class of backgrounds, a transition to the
flat vacuum state during inflation is effectively prevented by the rapidly
expanding orbifold. We demonstrate that such a transition can be realized for
solutions where one boundary potential is negative. For this case, we present
two concrete inflationary models which exhibit the transition explicitly.
