Offset-free setpoint tracking using neural network controllers

TL;DR

This paper develops a stability analysis method for neural network controllers in offset-free setpoint tracking, providing ellipsoidal regions of attraction and enabling guaranteed tracking with setpoint changes.

Contribution

It introduces a novel stability verification approach using linear matrix inequalities for neural network controllers with offset-free tracking capabilities.

Findings

Verified stability and offset-free tracking on an inverted pendulum example.

Derived less conservative local stability conditions for setpoint changes.

Provided ellipsoidal inner approximations of the region of attraction.

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.