Constrained nonlinear output regulation using model predictive control -- extended version

TL;DR

This paper introduces a novel MPC framework for constrained nonlinear output regulation that avoids classical offline solutions, ensuring stability and robustness through a new theoretical foundation and applicable to systems with unstable zero dynamics.

Contribution

It proposes a new MPC formulation for nonlinear output regulation that does not require solving regulator equations or using terminal costs, extending stability guarantees to a broader class of systems.

Findings

Ensures exponential stability for minimum phase systems.

Provides a design method for systems with unstable zero dynamics.

Establishes robustness properties under noisy output feedback.

Abstract

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.