On the Robustness of Data-Driven Controllers for Linear Systems

Rajasekhar Anguluri, Abed Alrahman Al Makdah, Vaibhav Katewa, Fabio Pasqualetti
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:404-412, 2020.

Abstract

This paper proposes a new framework and several results to quantify the performance of data-driven state-feedback controllers for linear systems against targeted perturbations of the training data. We focus on the case where subsets of the training data are randomly corrupted by an adversary, and derive lower and upper bounds for the stability of the closed-loop system with compromised controller as a function of the perturbation statistics, size of the training data, sensitivity of the data-driven algorithm to perturbation of the training data, and properties of the nominal closed-loop system. Our stability and convergence bounds are probabilistic in nature, and rely on a first-order approximation of the data-driven procedure that designs the state-feedback controller, which can be computed directly using the training data. We illustrate our findings via multiple numerical studies.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-anguluri20a, title = {On the Robustness of Data-Driven Controllers for Linear Systems}, author = {Anguluri, Rajasekhar and Makdah, Abed Alrahman Al and Katewa, Vaibhav and Pasqualetti, Fabio}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {404--412}, year = {2020}, editor = {Bayen, Alexandre M. and Jadbabaie, Ali and Pappas, George and Parrilo, Pablo A. and Recht, Benjamin and Tomlin, Claire and Zeilinger, Melanie}, volume = {120}, series = {Proceedings of Machine Learning Research}, month = {10--11 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v120/anguluri20a/anguluri20a.pdf}, url = {https://proceedings.mlr.press/v120/anguluri20a.html}, abstract = {This paper proposes a new framework and several results to quantify the performance of data-driven state-feedback controllers for linear systems against targeted perturbations of the training data. We focus on the case where subsets of the training data are randomly corrupted by an adversary, and derive lower and upper bounds for the stability of the closed-loop system with compromised controller as a function of the perturbation statistics, size of the training data, sensitivity of the data-driven algorithm to perturbation of the training data, and properties of the nominal closed-loop system. Our stability and convergence bounds are probabilistic in nature, and rely on a first-order approximation of the data-driven procedure that designs the state-feedback controller, which can be computed directly using the training data. We illustrate our findings via multiple numerical studies.} }
Endnote
%0 Conference Paper %T On the Robustness of Data-Driven Controllers for Linear Systems %A Rajasekhar Anguluri %A Abed Alrahman Al Makdah %A Vaibhav Katewa %A Fabio Pasqualetti %B Proceedings of the 2nd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2020 %E Alexandre M. Bayen %E Ali Jadbabaie %E George Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire Tomlin %E Melanie Zeilinger %F pmlr-v120-anguluri20a %I PMLR %P 404--412 %U https://proceedings.mlr.press/v120/anguluri20a.html %V 120 %X This paper proposes a new framework and several results to quantify the performance of data-driven state-feedback controllers for linear systems against targeted perturbations of the training data. We focus on the case where subsets of the training data are randomly corrupted by an adversary, and derive lower and upper bounds for the stability of the closed-loop system with compromised controller as a function of the perturbation statistics, size of the training data, sensitivity of the data-driven algorithm to perturbation of the training data, and properties of the nominal closed-loop system. Our stability and convergence bounds are probabilistic in nature, and rely on a first-order approximation of the data-driven procedure that designs the state-feedback controller, which can be computed directly using the training data. We illustrate our findings via multiple numerical studies.
APA
Anguluri, R., Makdah, A.A.A., Katewa, V. & Pasqualetti, F.. (2020). On the Robustness of Data-Driven Controllers for Linear Systems. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:404-412 Available from https://proceedings.mlr.press/v120/anguluri20a.html.

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