Data-driven Control of Unknown Linear Systems via Quantized Feedback

Feiran Zhao, Xingchen Li, Keyou You
Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:467-479, 2022.

Abstract

Control using quantized feedback is a fundamental approach to system synthesis with limited communication capacity. In this paper, we address the stabilization problem for unknown linear systems with logarithmically quantized feedback, via a direct data-driven control method. By leveraging a recently developed matrix S-lemma, we prove a sufficient and necessary condition for the existence of a common stabilizing controller for all possible dynamics consistent with data, in the form of a linear matrix inequality. Moreover, we formulate a semi-definite programming problem to solve the coarsest quantization density. By establishing its connections to unstable eigenvalues of the state matrix, we further prove a necessary rank condition on the data for quantized feedback stabilization. Finally, we validate our theoretical results by numerical examples.

Cite this Paper

BibTeX
@InProceedings{pmlr-v168-zhao22a, title = {Data-driven Control of Unknown Linear Systems via Quantized Feedback}, author = {Zhao, Feiran and Li, Xingchen and You, Keyou}, booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference}, pages = {467--479}, year = {2022}, editor = {Firoozi, Roya and Mehr, Negar and Yel, Esen and Antonova, Rika and Bohg, Jeannette and Schwager, Mac and Kochenderfer, Mykel}, volume = {168}, series = {Proceedings of Machine Learning Research}, month = {23--24 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v168/zhao22a/zhao22a.pdf}, url = {https://proceedings.mlr.press/v168/zhao22a.html}, abstract = {Control using quantized feedback is a fundamental approach to system synthesis with limited communication capacity. In this paper, we address the stabilization problem for unknown linear systems with logarithmically quantized feedback, via a direct data-driven control method. By leveraging a recently developed matrix S-lemma, we prove a sufficient and necessary condition for the existence of a common stabilizing controller for all possible dynamics consistent with data, in the form of a linear matrix inequality. Moreover, we formulate a semi-definite programming problem to solve the coarsest quantization density. By establishing its connections to unstable eigenvalues of the state matrix, we further prove a necessary rank condition on the data for quantized feedback stabilization. Finally, we validate our theoretical results by numerical examples.} }
Endnote
%0 Conference Paper %T Data-driven Control of Unknown Linear Systems via Quantized Feedback %A Feiran Zhao %A Xingchen Li %A Keyou You %B Proceedings of The 4th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2022 %E Roya Firoozi %E Negar Mehr %E Esen Yel %E Rika Antonova %E Jeannette Bohg %E Mac Schwager %E Mykel Kochenderfer %F pmlr-v168-zhao22a %I PMLR %P 467--479 %U https://proceedings.mlr.press/v168/zhao22a.html %V 168 %X Control using quantized feedback is a fundamental approach to system synthesis with limited communication capacity. In this paper, we address the stabilization problem for unknown linear systems with logarithmically quantized feedback, via a direct data-driven control method. By leveraging a recently developed matrix S-lemma, we prove a sufficient and necessary condition for the existence of a common stabilizing controller for all possible dynamics consistent with data, in the form of a linear matrix inequality. Moreover, we formulate a semi-definite programming problem to solve the coarsest quantization density. By establishing its connections to unstable eigenvalues of the state matrix, we further prove a necessary rank condition on the data for quantized feedback stabilization. Finally, we validate our theoretical results by numerical examples.
APA
Zhao, F., Li, X. & You, K.. (2022). Data-driven Control of Unknown Linear Systems via Quantized Feedback. Proceedings of The 4th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 168:467-479 Available from https://proceedings.mlr.press/v168/zhao22a.html.

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