Deep model-free KKL observer: A switching approach

Johan Peralez, Madiha Nadri
Proceedings of the 6th Annual Learning for Dynamics & Control Conference, PMLR 242:929-940, 2024.

Abstract

This paper presents a new model-free methodology to learn Kazantzis-Kravaris-Luenberger (KKL) observers for nonlinear systems. We address three major difficulties arising in observer design: the peaking phenomenon, the noise sensitivity and the trade-off between convergence speed and robustness. We formulate the learning objective as an optimization problem, strictly minimizing the error of the observer estimates, without the need of adding explicit constraints or regularization terms. We further improve the performance with a switching approach, efficiently transitioning between two observers, respectively designed for the transient phase and the asymptotic convergence. Numerical results on the Van der Pol system, the Rössler attractor and on a bioreactor illustrate the gain of the method regarding the literature, in term of performance and robustness. Code available online: https://github.com/jolindien-git/DeepKKL

Cite this Paper

BibTeX
@InProceedings{pmlr-v242-peralez24a, title = {Deep model-free {KKL} observer: {A} switching approach}, author = {Peralez, Johan and Nadri, Madiha}, booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference}, pages = {929--940}, year = {2024}, editor = {Abate, Alessandro and Cannon, Mark and Margellos, Kostas and Papachristodoulou, Antonis}, volume = {242}, series = {Proceedings of Machine Learning Research}, month = {15--17 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v242/peralez24a/peralez24a.pdf}, url = {https://proceedings.mlr.press/v242/peralez24a.html}, abstract = {This paper presents a new model-free methodology to learn Kazantzis-Kravaris-Luenberger (KKL) observers for nonlinear systems. We address three major difficulties arising in observer design: the peaking phenomenon, the noise sensitivity and the trade-off between convergence speed and robustness. We formulate the learning objective as an optimization problem, strictly minimizing the error of the observer estimates, without the need of adding explicit constraints or regularization terms. We further improve the performance with a switching approach, efficiently transitioning between two observers, respectively designed for the transient phase and the asymptotic convergence. Numerical results on the Van der Pol system, the Rössler attractor and on a bioreactor illustrate the gain of the method regarding the literature, in term of performance and robustness. Code available online: https://github.com/jolindien-git/DeepKKL} }
Endnote
%0 Conference Paper %T Deep model-free KKL observer: A switching approach %A Johan Peralez %A Madiha Nadri %B Proceedings of the 6th Annual Learning for Dynamics & Control Conference %C Proceedings of Machine Learning Research %D 2024 %E Alessandro Abate %E Mark Cannon %E Kostas Margellos %E Antonis Papachristodoulou %F pmlr-v242-peralez24a %I PMLR %P 929--940 %U https://proceedings.mlr.press/v242/peralez24a.html %V 242 %X This paper presents a new model-free methodology to learn Kazantzis-Kravaris-Luenberger (KKL) observers for nonlinear systems. We address three major difficulties arising in observer design: the peaking phenomenon, the noise sensitivity and the trade-off between convergence speed and robustness. We formulate the learning objective as an optimization problem, strictly minimizing the error of the observer estimates, without the need of adding explicit constraints or regularization terms. We further improve the performance with a switching approach, efficiently transitioning between two observers, respectively designed for the transient phase and the asymptotic convergence. Numerical results on the Van der Pol system, the Rössler attractor and on a bioreactor illustrate the gain of the method regarding the literature, in term of performance and robustness. Code available online: https://github.com/jolindien-git/DeepKKL
APA
Peralez, J. & Nadri, M.. (2024). Deep model-free KKL observer: A switching approach. Proceedings of the 6th Annual Learning for Dynamics & Control Conference, in Proceedings of Machine Learning Research 242:929-940 Available from https://proceedings.mlr.press/v242/peralez24a.html.

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