Stability of Certainty-Equivalent Adaptive LQR for Linear Systems with Unknown Time-Varying Parameters

Marcell Bartos, Johannes Köhler, Florian Dorfler, Melanie Zeilinger
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:1363-1381, 2026.

Abstract

Standard model-based control design deteriorates when the system dynamics change during operation. To overcome this challenge, online and adaptive methods have been proposed in the literature. In this work, we consider the class of discrete-time linear systems with unknown time-varying parameters. We propose a simple, modular, and computationally tractable approach by combining two classical and well-known building blocks from estimation and control: the least mean square filter and the certainty-equivalent linear quadratic regulator. Despite both building blocks being simple and off-the-shelf, our analysis shows that they can be seamlessly combined to a powerful pipeline with stability guarantees. Namely, finite-gain $\ell^2$-stability of the closed-loop interconnection of the unknown system, the parameter estimator, and the controller is proven, despite the presence of unknown disturbances and time-varying parametric uncertainties. Real-world applicability of the proposed algorithm is showcased by simulations carried out on a nonlinear planar quadrotor.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-bartos26a, title = {Stability of Certainty-Equivalent Adaptive LQR for Linear Systems with Unknown Time-Varying Parameters}, author = {Bartos, Marcell and K\"ohler, Johannes and Dorfler, Florian and Zeilinger, Melanie}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {1363--1381}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/bartos26a/bartos26a.pdf}, url = {https://proceedings.mlr.press/v331/bartos26a.html}, abstract = {Standard model-based control design deteriorates when the system dynamics change during operation. To overcome this challenge, online and adaptive methods have been proposed in the literature. In this work, we consider the class of discrete-time linear systems with unknown time-varying parameters. We propose a simple, modular, and computationally tractable approach by combining two classical and well-known building blocks from estimation and control: the least mean square filter and the certainty-equivalent linear quadratic regulator. Despite both building blocks being simple and off-the-shelf, our analysis shows that they can be seamlessly combined to a powerful pipeline with stability guarantees. Namely, finite-gain $\ell^2$-stability of the closed-loop interconnection of the unknown system, the parameter estimator, and the controller is proven, despite the presence of unknown disturbances and time-varying parametric uncertainties. Real-world applicability of the proposed algorithm is showcased by simulations carried out on a nonlinear planar quadrotor.} }
Endnote
%0 Conference Paper %T Stability of Certainty-Equivalent Adaptive LQR for Linear Systems with Unknown Time-Varying Parameters %A Marcell Bartos %A Johannes Köhler %A Florian Dorfler %A Melanie Zeilinger %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-bartos26a %I PMLR %P 1363--1381 %U https://proceedings.mlr.press/v331/bartos26a.html %V 331 %X Standard model-based control design deteriorates when the system dynamics change during operation. To overcome this challenge, online and adaptive methods have been proposed in the literature. In this work, we consider the class of discrete-time linear systems with unknown time-varying parameters. We propose a simple, modular, and computationally tractable approach by combining two classical and well-known building blocks from estimation and control: the least mean square filter and the certainty-equivalent linear quadratic regulator. Despite both building blocks being simple and off-the-shelf, our analysis shows that they can be seamlessly combined to a powerful pipeline with stability guarantees. Namely, finite-gain $\ell^2$-stability of the closed-loop interconnection of the unknown system, the parameter estimator, and the controller is proven, despite the presence of unknown disturbances and time-varying parametric uncertainties. Real-world applicability of the proposed algorithm is showcased by simulations carried out on a nonlinear planar quadrotor.
APA
Bartos, M., Köhler, J., Dorfler, F. & Zeilinger, M.. (2026). Stability of Certainty-Equivalent Adaptive LQR for Linear Systems with Unknown Time-Varying Parameters. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:1363-1381 Available from https://proceedings.mlr.press/v331/bartos26a.html.

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