Adaptive Nonlinear Regulation via Gaussian Process

TL;DR

This paper introduces a novel adaptive nonlinear regulation method using Gaussian process regression, enabling more flexible and smooth control without finite-dimensional model assumptions, demonstrated through numerical simulations.

Contribution

It extends adaptive internal model design with Gaussian processes, allowing regulation with only smoothness assumptions on the steady-state control.

Findings

Outperforms previous methods in simulations

Requires only smoothness of steady-state control

Uses event-triggered learning for adaptation

Abstract

The paper deals with the problem of output regulation of nonlinear systems by presenting a learning-based adaptive internal model-based design strategy. We borrow from the adaptive internal model design technique recently proposed in [1] and extend it by means of a Gaussian process regressor. The learning-based adaptation is performed by following an "event-triggered" logic so that hybrid tools are used to analyse the resulting closed-loop system. Unlike the approach proposed in [1] where the friend is supposed to belong to a specific finite-dimensional model set, here we only require smoothness of the ideal steady-state control action. The paper also presents numerical simulations showing how the proposed method outperforms previous approaches.