Data-Driven System Level Synthesis

Anton Xue, Nikolai Matni
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:189-200, 2021.

Abstract

We establish data-driven versions of the System Level Synthesis (SLS) parameterization of stabilizing controllers for linear-time-invariant systems. Inspired by recent work in data-driven control that leverages tools from behavioral theory, we show that optimization problems over system-responses can be posed using only libraries of past system trajectories, without explicitly identifying a system model. We first consider the idealized setting of noise free trajectories, and show an exact equivalence between traditional and data-driven SLS. We then show that in the case of a system driven by process noise, tools from robust SLS can be used to characterize the effects of noise on closed-loop performance. We then draw on tools from matrix concentration to show that a simple trajectory averaging technique can be used to mitigate these effects. We end with numerical experiments showing the soundness of our methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-xue21a, title = {Data-Driven System Level Synthesis}, author = {Xue, Anton and Matni, Nikolai}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {189--200}, 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/xue21a/xue21a.pdf}, url = {https://proceedings.mlr.press/v144/xue21a.html}, abstract = {We establish data-driven versions of the System Level Synthesis (SLS) parameterization of stabilizing controllers for linear-time-invariant systems. Inspired by recent work in data-driven control that leverages tools from behavioral theory, we show that optimization problems over system-responses can be posed using only libraries of past system trajectories, without explicitly identifying a system model. We first consider the idealized setting of noise free trajectories, and show an exact equivalence between traditional and data-driven SLS. We then show that in the case of a system driven by process noise, tools from robust SLS can be used to characterize the effects of noise on closed-loop performance. We then draw on tools from matrix concentration to show that a simple trajectory averaging technique can be used to mitigate these effects. We end with numerical experiments showing the soundness of our methods.} }
Endnote
%0 Conference Paper %T Data-Driven System Level Synthesis %A Anton Xue %A Nikolai Matni %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-xue21a %I PMLR %P 189--200 %U https://proceedings.mlr.press/v144/xue21a.html %V 144 %X We establish data-driven versions of the System Level Synthesis (SLS) parameterization of stabilizing controllers for linear-time-invariant systems. Inspired by recent work in data-driven control that leverages tools from behavioral theory, we show that optimization problems over system-responses can be posed using only libraries of past system trajectories, without explicitly identifying a system model. We first consider the idealized setting of noise free trajectories, and show an exact equivalence between traditional and data-driven SLS. We then show that in the case of a system driven by process noise, tools from robust SLS can be used to characterize the effects of noise on closed-loop performance. We then draw on tools from matrix concentration to show that a simple trajectory averaging technique can be used to mitigate these effects. We end with numerical experiments showing the soundness of our methods.
APA
Xue, A. & Matni, N.. (2021). Data-Driven System Level Synthesis. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:189-200 Available from https://proceedings.mlr.press/v144/xue21a.html.

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