  We present a model predictive control (MPC) framework to solve the
constrained nonlinear output regulation problem. The main feature of the
proposed framework is that the application does not require the solution to
classical regulator (Francis-Byrnes-Isidori) equations or any other offline
design procedure. In particular, the proposed formulation simply minimizes the
predicted output error, possibly with some input regularization. Instead of
using terminal cost/sets or a positive definite stage cost as is standard in
MPC theory, we build on the theoretical results by Grimm et al. 2005 using a
detectability notion. The proposed formulation is applicable if the constrained
nonlinear regulation problem is (strictly) feasible, the plant is incrementally
stabilizable and incrementally input-output to state stable
(i-IOSS/detectable). We show that for minimum phase systems such a design
ensures exponential stability of the regulator manifold. We also provide a
design procedure in case of unstable zero dynamics using an incremental input
regularization and a nonresonance condition. Inherent robustness properties for
the noisy error/output-feedback case are established under simplifying
assumptions (e.g. no state constraints). The theoretical results are
illustrated with an example involving offset free tracking with noisy error
feedback. The paper also contains novel results for MPC without terminal
constraints with positive semidefinite input/output stage costs that are of
independent interest.
