Data-driven robust covariance control for uncertain linear systems

Joshua Pilipovsky, Panagiotis Tsiotras
Proceedings of the 6th Annual Learning for Dynamics & Control Conference, PMLR 242:667-678, 2024.

Abstract

The theory of covariance control and covariance steering (CS) deals with controlling the dispersion of trajectories of a dynamical system, under the implicit assumption that accurate prior knowledge of the system being controlled is available. In this work, we consider the problem of steering the distribution of a discrete-time, linear system subject to exogenous disturbances under an unknown dynamics model. Leveraging concepts from behavioral systems theory, the trajectories of this unknown, noisy system may be (approximately) represented using system data collected through experimentation. Using this fact, we formulate a direct data-driven covariance control problem using input-state data. We then propose a maximum likelihood uncertainty quantification method to estimate and bound the noise realizations in the data collection process. Lastly, we utilize robust convex optimization techniques to solve the resulting norm-bounded uncertain convex program. We illustrate the proposed end-to-end data-driven CS algorithm on a double integrator example and showcase the efficacy and accuracy of the proposed method compared to that of model-based methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v242-pilipovsky24a, title = {Data-driven robust covariance control for uncertain linear systems}, author = {Pilipovsky, Joshua and Tsiotras, Panagiotis}, booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference}, pages = {667--678}, year = {2024}, editor = {Abate, Alessandro and Cannon, Mark and Margellos, Kostas and Papachristodoulou, Antonis}, volume = {242}, series = {Proceedings of Machine Learning Research}, month = {15--17 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v242/pilipovsky24a/pilipovsky24a.pdf}, url = {https://proceedings.mlr.press/v242/pilipovsky24a.html}, abstract = {The theory of covariance control and covariance steering (CS) deals with controlling the dispersion of trajectories of a dynamical system, under the implicit assumption that accurate prior knowledge of the system being controlled is available. In this work, we consider the problem of steering the distribution of a discrete-time, linear system subject to exogenous disturbances under an unknown dynamics model. Leveraging concepts from behavioral systems theory, the trajectories of this unknown, noisy system may be (approximately) represented using system data collected through experimentation. Using this fact, we formulate a direct data-driven covariance control problem using input-state data. We then propose a maximum likelihood uncertainty quantification method to estimate and bound the noise realizations in the data collection process. Lastly, we utilize robust convex optimization techniques to solve the resulting norm-bounded uncertain convex program. We illustrate the proposed end-to-end data-driven CS algorithm on a double integrator example and showcase the efficacy and accuracy of the proposed method compared to that of model-based methods.} }
Endnote
%0 Conference Paper %T Data-driven robust covariance control for uncertain linear systems %A Joshua Pilipovsky %A Panagiotis Tsiotras %B Proceedings of the 6th Annual Learning for Dynamics & Control Conference %C Proceedings of Machine Learning Research %D 2024 %E Alessandro Abate %E Mark Cannon %E Kostas Margellos %E Antonis Papachristodoulou %F pmlr-v242-pilipovsky24a %I PMLR %P 667--678 %U https://proceedings.mlr.press/v242/pilipovsky24a.html %V 242 %X The theory of covariance control and covariance steering (CS) deals with controlling the dispersion of trajectories of a dynamical system, under the implicit assumption that accurate prior knowledge of the system being controlled is available. In this work, we consider the problem of steering the distribution of a discrete-time, linear system subject to exogenous disturbances under an unknown dynamics model. Leveraging concepts from behavioral systems theory, the trajectories of this unknown, noisy system may be (approximately) represented using system data collected through experimentation. Using this fact, we formulate a direct data-driven covariance control problem using input-state data. We then propose a maximum likelihood uncertainty quantification method to estimate and bound the noise realizations in the data collection process. Lastly, we utilize robust convex optimization techniques to solve the resulting norm-bounded uncertain convex program. We illustrate the proposed end-to-end data-driven CS algorithm on a double integrator example and showcase the efficacy and accuracy of the proposed method compared to that of model-based methods.
APA
Pilipovsky, J. & Tsiotras, P.. (2024). Data-driven robust covariance control for uncertain linear systems. Proceedings of the 6th Annual Learning for Dynamics & Control Conference, in Proceedings of Machine Learning Research 242:667-678 Available from https://proceedings.mlr.press/v242/pilipovsky24a.html.

Related Material