Stable Online Control of Linear Time-Varying Systems

Guannan Qu, Yuanyuan Shi, Sahin Lale, Anima Anandkumar, Adam Wierman
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:742-753, 2021.

Abstract

Linear time-varying (LTV) systems are widely used for modeling real-world dynamical systems due to their generality and simplicity. Providing stability guarantees for LTV systems is one of the central problems in control theory. However, existing approaches that guarantee stability typically lead to significantly sub-optimal cumulative control cost in online settings where only current or short-term system information is available. In this work, we propose an efficient online control algorithm, COvariance Constrained Online Linear Quadratic (COCO-LQ) control, that guarantees input-to-state stability for a large class of LTV systems while also minimizing the control cost. The proposed method incorporates a state covariance constraint into the semi-definite programming (SDP) formulation of the LQ optimal controller. We empirically demonstrate the performance of COCO-LQ in both synthetic experiments and a power system frequency control example.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-qu21a, title = {Stable Online Control of Linear Time-Varying Systems}, author = {Qu, Guannan and Shi, Yuanyuan and Lale, Sahin and Anandkumar, Anima and Wierman, Adam}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {742--753}, 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/qu21a/qu21a.pdf}, url = {https://proceedings.mlr.press/v144/qu21a.html}, abstract = {Linear time-varying (LTV) systems are widely used for modeling real-world dynamical systems due to their generality and simplicity. Providing stability guarantees for LTV systems is one of the central problems in control theory. However, existing approaches that guarantee stability typically lead to significantly sub-optimal cumulative control cost in online settings where only current or short-term system information is available. In this work, we propose an efficient online control algorithm, COvariance Constrained Online Linear Quadratic (COCO-LQ) control, that guarantees input-to-state stability for a large class of LTV systems while also minimizing the control cost. The proposed method incorporates a state covariance constraint into the semi-definite programming (SDP) formulation of the LQ optimal controller. We empirically demonstrate the performance of COCO-LQ in both synthetic experiments and a power system frequency control example. } }
Endnote
%0 Conference Paper %T Stable Online Control of Linear Time-Varying Systems %A Guannan Qu %A Yuanyuan Shi %A Sahin Lale %A Anima Anandkumar %A Adam Wierman %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-qu21a %I PMLR %P 742--753 %U https://proceedings.mlr.press/v144/qu21a.html %V 144 %X Linear time-varying (LTV) systems are widely used for modeling real-world dynamical systems due to their generality and simplicity. Providing stability guarantees for LTV systems is one of the central problems in control theory. However, existing approaches that guarantee stability typically lead to significantly sub-optimal cumulative control cost in online settings where only current or short-term system information is available. In this work, we propose an efficient online control algorithm, COvariance Constrained Online Linear Quadratic (COCO-LQ) control, that guarantees input-to-state stability for a large class of LTV systems while also minimizing the control cost. The proposed method incorporates a state covariance constraint into the semi-definite programming (SDP) formulation of the LQ optimal controller. We empirically demonstrate the performance of COCO-LQ in both synthetic experiments and a power system frequency control example.
APA
Qu, G., Shi, Y., Lale, S., Anandkumar, A. & Wierman, A.. (2021). Stable Online Control of Linear Time-Varying Systems. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:742-753 Available from https://proceedings.mlr.press/v144/qu21a.html.

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