Designing System Level Synthesis Controllers for Nonlinear Systems with Stability Guarantees

Lauren E Conger, Sydney Vernon, Eric Mazumdar
Proceedings of The 5th Annual Learning for Dynamics and Control Conference, PMLR 211:420-430, 2023.

Abstract

We introduce a method for controlling systems with nonlinear dynamics and full actuation by approximating the dynamics with polynomials and applying a system level synthesis controller. We show how to optimize over this class of controllers using a neural network while maintaining stability guarantees, without requiring a Lyapunov function. We give bounds for the domain over which the use of the class of controllers preserves stability and gives bounds on the control costs incurred by optimized controllers. We then numerically validate our approach and show improved performance compared with feedback linearization— suggesting that the SLS controllers are able to take advantage of nonlinearities in the dynamics while guaranteeing stability.

Cite this Paper

BibTeX
@InProceedings{pmlr-v211-conger23a, title = {Designing System Level Synthesis Controllers for Nonlinear Systems with Stability Guarantees}, author = {Conger, Lauren E and Vernon, Sydney and Mazumdar, Eric}, booktitle = {Proceedings of The 5th Annual Learning for Dynamics and Control Conference}, pages = {420--430}, year = {2023}, editor = {Matni, Nikolai and Morari, Manfred and Pappas, George J.}, volume = {211}, series = {Proceedings of Machine Learning Research}, month = {15--16 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v211/conger23a/conger23a.pdf}, url = {https://proceedings.mlr.press/v211/conger23a.html}, abstract = {We introduce a method for controlling systems with nonlinear dynamics and full actuation by approximating the dynamics with polynomials and applying a system level synthesis controller. We show how to optimize over this class of controllers using a neural network while maintaining stability guarantees, without requiring a Lyapunov function. We give bounds for the domain over which the use of the class of controllers preserves stability and gives bounds on the control costs incurred by optimized controllers. We then numerically validate our approach and show improved performance compared with feedback linearization— suggesting that the SLS controllers are able to take advantage of nonlinearities in the dynamics while guaranteeing stability.} }
Endnote
%0 Conference Paper %T Designing System Level Synthesis Controllers for Nonlinear Systems with Stability Guarantees %A Lauren E Conger %A Sydney Vernon %A Eric Mazumdar %B Proceedings of The 5th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2023 %E Nikolai Matni %E Manfred Morari %E George J. Pappas %F pmlr-v211-conger23a %I PMLR %P 420--430 %U https://proceedings.mlr.press/v211/conger23a.html %V 211 %X We introduce a method for controlling systems with nonlinear dynamics and full actuation by approximating the dynamics with polynomials and applying a system level synthesis controller. We show how to optimize over this class of controllers using a neural network while maintaining stability guarantees, without requiring a Lyapunov function. We give bounds for the domain over which the use of the class of controllers preserves stability and gives bounds on the control costs incurred by optimized controllers. We then numerically validate our approach and show improved performance compared with feedback linearization— suggesting that the SLS controllers are able to take advantage of nonlinearities in the dynamics while guaranteeing stability.
APA
Conger, L.E., Vernon, S. & Mazumdar, E.. (2023). Designing System Level Synthesis Controllers for Nonlinear Systems with Stability Guarantees. Proceedings of The 5th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 211:420-430 Available from https://proceedings.mlr.press/v211/conger23a.html.

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