# Offset-free setpoint tracking using neural network controllers

arXiv: https://arxiv.org/abs/2011.14006 · HTML: https://mlsanity.com/paper/2011.14006/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2020.

## Built on by (most cited first, 10 of 10)

- [Imitation Learning with Stability and Safety Guarantees](https://mlsanity.com/paper/2012.09293/) (2020)
- [Distributed neural network control with dependability guarantees: a compositional port-Hamiltonian approach](https://mlsanity.com/paper/2112.09046/) (2021)
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- [Neural System Level Synthesis: Learning over All Stabilizing Policies for Nonlinear Systems](https://mlsanity.com/paper/2203.11812/) (2022)
- [Learning to Boost the Performance of Stable Nonlinear Systems](https://mlsanity.com/paper/2405.00871/) (2024)
- [Linear systems with neural network nonlinearities: Improved stability analysis via acausal Zames-Falb multipliers](https://mlsanity.com/paper/2103.17106/) (2021)
- [Convolutional Neural Networks as 2-D systems](https://mlsanity.com/paper/2303.03042/) (2023)
- [Neural Observer with Lyapunov Stability Guarantee for Uncertain Nonlinear Systems](https://mlsanity.com/paper/2208.13006/) (2022)
- [Dissipative Imitation Learning for Robust Dynamic Output Feedback](https://mlsanity.com/paper/2210.00979/) (2022)
- [Dissipative Imitation Learning for Discrete Dynamic Output Feedback Control with Sparse Data Sets](https://mlsanity.com/paper/2309.06658/) (2023)

## Abstract (arXiv)

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.