Offset-free setpoint tracking using neural network controllers
Abstract
In this paper, we present a method to analyze local and global stability in offset-free setpoint tracking using neural network controllers and we provide ellipsoidal inner approximations of the corresponding region of attraction. We consider a feedback interconnection of a linear plant in connection with a neural network controller and an integrator, which allows for offset-free tracking of a desired piecewise constant reference that enters the controller as an external input. Exploiting the fact that activation functions used in neural networks are slope-restricted, we derive linear matrix inequalities to verify stability using Lyapunov theory. After stating a global stability result, we present less conservative local stability conditions (i) for a given reference and (ii) for any reference from a certain set. The latter result even enables guaranteed tracking under setpoint changes using a reference governor which can lead to a significant increase of the region of attraction. Finally, we demonstrate the applicability of our analysis by verifying stability and offset-free tracking of a neural network controller that was trained to stabilize a linearized inverted pendulum.
Cite
@article{arxiv.2011.14006,
title = {Offset-free setpoint tracking using neural network controllers},
author = {Patricia Pauli and Johannes Köhler and Julian Berberich and Anne Koch and Frank Allgöwer},
journal= {arXiv preprint arXiv:2011.14006},
year = {2021}
}