Data-Driven Controller Design via Finite-Horizon Dissipativity

Nils Wieler, Julian Berberich, Anne Koch, Frank Allgöwer
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:287-298, 2021.

Abstract

Given a single measured trajectory of a discrete-time linear time-invariant system, we present a framework for data-driven controller design for closed-loop finite-horizon dissipativity. First we parametrize all closed-loop trajectories using the given data of the plant and a model of the controller. We then provide an approach to validate the controller by verifying closed-loop dissipativity in the standard feedback loop based on this parametrization. The developed conditions allow us to state the corresponding controller synthesis problem as a quadratic matrix inequality feasibility problem. Hence, we obtain purely data-driven synthesis conditions leading to a desired closed-loop dissipativity property. Finally, the results are illustrated with a simulation example.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-wieler21a, title = {Data-Driven Controller Design via Finite-Horizon Dissipativity}, author = {Wieler, Nils and Berberich, Julian and Koch, Anne and Allg\"ower, Frank}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {287--298}, 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/wieler21a/wieler21a.pdf}, url = {https://proceedings.mlr.press/v144/wieler21a.html}, abstract = {Given a single measured trajectory of a discrete-time linear time-invariant system, we present a framework for data-driven controller design for closed-loop finite-horizon dissipativity. First we parametrize all closed-loop trajectories using the given data of the plant and a model of the controller. We then provide an approach to validate the controller by verifying closed-loop dissipativity in the standard feedback loop based on this parametrization. The developed conditions allow us to state the corresponding controller synthesis problem as a quadratic matrix inequality feasibility problem. Hence, we obtain purely data-driven synthesis conditions leading to a desired closed-loop dissipativity property. Finally, the results are illustrated with a simulation example.} }
Endnote
%0 Conference Paper %T Data-Driven Controller Design via Finite-Horizon Dissipativity %A Nils Wieler %A Julian Berberich %A Anne Koch %A Frank Allgöwer %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-wieler21a %I PMLR %P 287--298 %U https://proceedings.mlr.press/v144/wieler21a.html %V 144 %X Given a single measured trajectory of a discrete-time linear time-invariant system, we present a framework for data-driven controller design for closed-loop finite-horizon dissipativity. First we parametrize all closed-loop trajectories using the given data of the plant and a model of the controller. We then provide an approach to validate the controller by verifying closed-loop dissipativity in the standard feedback loop based on this parametrization. The developed conditions allow us to state the corresponding controller synthesis problem as a quadratic matrix inequality feasibility problem. Hence, we obtain purely data-driven synthesis conditions leading to a desired closed-loop dissipativity property. Finally, the results are illustrated with a simulation example.
APA
Wieler, N., Berberich, J., Koch, A. & Allgöwer, F.. (2021). Data-Driven Controller Design via Finite-Horizon Dissipativity. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:287-298 Available from https://proceedings.mlr.press/v144/wieler21a.html.

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