Data-driven Identification of Approximate Passive Linear Models for Nonlinear Systems

S. Sivaranjani, Etika Agarwal, Vijay Gupta
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:338-339, 2020.

Abstract

In model-based learning, it is desirable for the learned model to preserve structural properties of the system that may facilitate easier control design or provide performance, stability or safety guarantees. Here, we consider an unknown nonlinear system possessing such a structural property - passivity, that can be used to ensure robust stability with a learned controller. We present an algorithm to learn a passive linear model of this nonlinear system from time domain input-output data. We first learn an approximate linear model of this system using any standard system identification technique. We then enforce passivity by perturbing the system matrices of the linear model, while ensuring that the perturbed model closely approximates the input-output behavior of the nonlinear system. Finally, we derive a trade-off between the perturbation size and the radius of the region in which the passivity of the linear model guarantees local passivity of the unknown nonlinear system.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-sivaranjani20a, title = {Data-driven Identification of Approximate Passive Linear Models for Nonlinear Systems}, author = {Sivaranjani, S. and Agarwal, Etika and Gupta, Vijay}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {338--339}, 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/sivaranjani20a/sivaranjani20a.pdf}, url = {https://proceedings.mlr.press/v120/sivaranjani20a.html}, abstract = {In model-based learning, it is desirable for the learned model to preserve structural properties of the system that may facilitate easier control design or provide performance, stability or safety guarantees. Here, we consider an unknown nonlinear system possessing such a structural property - passivity, that can be used to ensure robust stability with a learned controller. We present an algorithm to learn a passive linear model of this nonlinear system from time domain input-output data. We first learn an approximate linear model of this system using any standard system identification technique. We then enforce passivity by perturbing the system matrices of the linear model, while ensuring that the perturbed model closely approximates the input-output behavior of the nonlinear system. Finally, we derive a trade-off between the perturbation size and the radius of the region in which the passivity of the linear model guarantees local passivity of the unknown nonlinear system. } }
Endnote
%0 Conference Paper %T Data-driven Identification of Approximate Passive Linear Models for Nonlinear Systems %A S. Sivaranjani %A Etika Agarwal %A Vijay Gupta %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-sivaranjani20a %I PMLR %P 338--339 %U https://proceedings.mlr.press/v120/sivaranjani20a.html %V 120 %X In model-based learning, it is desirable for the learned model to preserve structural properties of the system that may facilitate easier control design or provide performance, stability or safety guarantees. Here, we consider an unknown nonlinear system possessing such a structural property - passivity, that can be used to ensure robust stability with a learned controller. We present an algorithm to learn a passive linear model of this nonlinear system from time domain input-output data. We first learn an approximate linear model of this system using any standard system identification technique. We then enforce passivity by perturbing the system matrices of the linear model, while ensuring that the perturbed model closely approximates the input-output behavior of the nonlinear system. Finally, we derive a trade-off between the perturbation size and the radius of the region in which the passivity of the linear model guarantees local passivity of the unknown nonlinear system.
APA
Sivaranjani, S., Agarwal, E. & Gupta, V.. (2020). Data-driven Identification of Approximate Passive Linear Models for Nonlinear Systems. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:338-339 Available from https://proceedings.mlr.press/v120/sivaranjani20a.html.

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