Data-Driven Nonlinear Regulation: Gaussian Process Learning

TL;DR

This paper presents a data-driven control method for nonlinear systems using Gaussian Process regression to learn internal models online, improving robustness and convergence without relying on traditional model-based observers.

Contribution

It introduces a novel output feedback controller that integrates Gaussian Process learning directly into the regulation framework, avoiding the need for model-based observers.

Findings

The method ensures boundedness and convergence of the closed-loop system.

The size of the convergence set decreases as the Gaussian Process model accuracy improves.

Numerical examples validate the effectiveness and robustness of the proposed approach.

Abstract

This article addresses the output regulation problem for a class of nonlinear systems using a data-driven approach. An output feedback controller is proposed that integrates a traditional control component with a data-driven learning algorithm based on Gaussian Process (GP) regression to learn the nonlinear internal model. Specifically, a data-driven technique is employed to directly approximate the unknown internal model steady-state map from observed input-output data online. Our method does not rely on model-based observers utilized in previous studies, making it robust and suitable for systems with modelling errors and model uncertainties. Finally, we demonstrate through numerical examples and detailed stability analysis that, under suitable conditions, the closed-loop system remains bounded and converges to a compact set, with the size of this set decreasing as the accuracy of the data-driven model improves over time.