Constrained Nonlinear Output Regulation Using Model Predictive Control

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. 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. The theoretical results are illustrated with an example involving offset-free tracking.

Automated summary

We propose a model predictive control framework that solves the constrained nonlinear output regulation problem without relying on classical regulator equations or offline design procedures. By minimizing predicted output error, we develop a formulation applicable to strictly feasible constrained nonlinear regulation problems. For minimum phase systems, this design ensures exponential stability of the regulator manifold. We also provide a design procedure for handling unstable zero dynamics.