Offset-free setpoint tracking using neural network controllers

Patricia Pauli, Johannes Köhler, Julian Berberich, Anne Koch, Frank Allgöwer
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:992-1003, 2021.

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 using a neural network controller in connection with an integrator, which allows for offset-free tracking of a desired piecewise constant reference that enters the controller as an external input. The feedback interconnection considered in this paper allows for general configurations of the neural network controller that include the special cases of output error and state feedback. 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 an inverted pendulum.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-pauli21a, title = {Offset-free setpoint tracking using neural network controllers}, author = {Pauli, Patricia and K\"ohler, Johannes and Berberich, Julian and Koch, Anne and Allg\"ower, Frank}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {992--1003}, year = {2021}, editor = {Jadbabaie, Ali and Lygeros, John and Pappas, George J. and A. Parrilo, Pablo and Recht, Benjamin and Tomlin, Claire J. and Zeilinger, Melanie N.}, volume = {144}, series = {Proceedings of Machine Learning Research}, month = {07 -- 08 June}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v144/pauli21a/pauli21a.pdf}, url = {https://proceedings.mlr.press/v144/pauli21a.html}, 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 using a neural network controller in connection with an integrator, which allows for offset-free tracking of a desired piecewise constant reference that enters the controller as an external input. The feedback interconnection considered in this paper allows for general configurations of the neural network controller that include the special cases of output error and state feedback. 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 an inverted pendulum.} }
Endnote
%0 Conference Paper %T Offset-free setpoint tracking using neural network controllers %A Patricia Pauli %A Johannes Köhler %A Julian Berberich %A Anne Koch %A Frank Allgöwer %B Proceedings of the 3rd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2021 %E Ali Jadbabaie %E John Lygeros %E George J. Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire J. Tomlin %E Melanie N. Zeilinger %F pmlr-v144-pauli21a %I PMLR %P 992--1003 %U https://proceedings.mlr.press/v144/pauli21a.html %V 144 %X 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 using a neural network controller in connection with an integrator, which allows for offset-free tracking of a desired piecewise constant reference that enters the controller as an external input. The feedback interconnection considered in this paper allows for general configurations of the neural network controller that include the special cases of output error and state feedback. 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 an inverted pendulum.
APA
Pauli, P., Köhler, J., Berberich, J., Koch, A. & Allgöwer, F.. (2021). Offset-free setpoint tracking using neural network controllers. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:992-1003 Available from https://proceedings.mlr.press/v144/pauli21a.html.

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