  We show that a special class of (nonconvex) NMPC problems admits an exact
solution by reformulating them as a finite number of convex subproblems,
extending previous results to the multi-input case. Our approach is applicable
to a special class of input-affine discrete-time systems, which includes a
class of bilinear rank-one systems that is considered useful in modeling
certain controlled networks. We illustrate our results with two numerical
examples, including the aforementioned rank-one bilinear network.
