  This paper presents an extension to the nonlinear Model Predictive Control
for Tracking scheme able to guarantee convergence even in cases of non-convex
output admissible sets. This is achieved by incorporating a convexifying
homeomorphism in the optimization problem, allowing it to be solved in the
convex space. A novel class of non-convex sets is also defined for which a
systematic procedure to construct a convexifying homeomorphism is provided.
This homeomorphism is then embedded in the Model Predictive Control
optimization problem in such a way that the homeomorphism is no longer required
in closed form. Finally, the effectiveness of the proposed method is showcased
through an illustrative example.
