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

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.

Extended version of accepted paper in Transaction on Automatic Control, 2021. Contains the following additional results: Exponential bounds on the suboptimality index using an observability condition and an extension of the derived theory to the noisy error feedback case

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• Constrained nonlinear output regulation using model predictive control -- extended version
• Convex Incremental Dissipativity Analysis of Nonlinear Systems - Extended version
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Cited by in corpus (5)

• Analysis and design of model predictive control frameworks for dynamic operation -- An overview
• Constrained nonlinear output regulation using model predictive control -- extended version
• Stability and performance analysis of NMPC: Detectable stage costs and general terminal costs
• Robust offset-free constrained Model Predictive Control with Long Short-Term Memory Networks -- Extended version
• Robust output feedback model predictive control using online estimation bounds