Convex NMPC reformulations for a special class of nonlinear multi-input systems with application to rank-one bilinear networks

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.