Stability of certainty-equivalent adaptive LQR for linear systems with unknown time-varying parameters
File(s)
Accepted version
Author(s)
Bartos, Marcell
Kohler, Johannes
Dörfler, Florian
Zeilinger, Melanie N
Type
Conference Paper
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 l²-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.
Date Issued
2026-06-19
Date Acceptance
2026-01-23
Citation
Proceedings of Machine Learning Research, 2026, 331, pp.1363-1381
ISSN
2640-3498
Publisher
MLResearchPress
Start Page
1363
End Page
1381
Journal / Book Title
Proceedings of Machine Learning Research
Volume
331
Copyright Statement
© 2026 M. Bartos, J. Kohler, F. Dorfler & M.N. Zeilinger. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Identifier
https://arxiv.org/abs/2511.08236v1
Source
8th Annual Learning for Dynamics & Control Conference (L4DC)
Subjects
eess.SY
eess.SY
math.OC
Publication Status
Published
Start Date
2026-06-17
Finish Date
2026-06-19
Coverage Spatial
Los Angeles, CA, USA
Date Publish Online
2026-06-19