  We show how the solution to NMPC problems for a special type of input-affine
discrete-time systems can be obtained by reformulating the underlying
non-convex optimal control problem in terms of a finite number of convex
subproblems. The reformulation is facilitated by exact (input-state)
linearization, which is shown to provide beneficial properties for the treated
class of systems. We characterize possible types of the resulting convex
subproblems and illustrate our approach with three numerical examples.
