Distributionally Robust Lyapunov Function Search Under Uncertainty

Kehan Long, Yinzhuang Yi, Jorge Cortes, Nikolay Atanasov
Proceedings of The 5th Annual Learning for Dynamics and Control Conference, PMLR 211:864-877, 2023.

Abstract

This paper develops methods for proving Lyapunov stability of dynamical systems subject to disturbances with an unknown distribution. We assume only a finite set of disturbance samples is available and that the true online disturbance realization may be drawn from a different distribution than the given samples. We formulate an optimization problem to search for a sum-of-squares (SOS) Lyapunov function and introduce a distributionally robust version of the Lyapunov function derivative constraint. We show that this constraint may be reformulated as several SOS constraints, ensuring that the search for a Lyapunov function remains in the class of SOS polynomial optimization problems. For general systems, we provide a distributionally robust chance-constrained formulation for neural network Lyapunov function search. Simulations demonstrate the validity and efficiency of either formulation on non-linear uncertain dynamical systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v211-long23a, title = {Distributionally Robust Lyapunov Function Search Under Uncertainty}, author = {Long, Kehan and Yi, Yinzhuang and Cortes, Jorge and Atanasov, Nikolay}, booktitle = {Proceedings of The 5th Annual Learning for Dynamics and Control Conference}, pages = {864--877}, 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/long23a/long23a.pdf}, url = {https://proceedings.mlr.press/v211/long23a.html}, abstract = {This paper develops methods for proving Lyapunov stability of dynamical systems subject to disturbances with an unknown distribution. We assume only a finite set of disturbance samples is available and that the true online disturbance realization may be drawn from a different distribution than the given samples. We formulate an optimization problem to search for a sum-of-squares (SOS) Lyapunov function and introduce a distributionally robust version of the Lyapunov function derivative constraint. We show that this constraint may be reformulated as several SOS constraints, ensuring that the search for a Lyapunov function remains in the class of SOS polynomial optimization problems. For general systems, we provide a distributionally robust chance-constrained formulation for neural network Lyapunov function search. Simulations demonstrate the validity and efficiency of either formulation on non-linear uncertain dynamical systems.} }
Endnote
%0 Conference Paper %T Distributionally Robust Lyapunov Function Search Under Uncertainty %A Kehan Long %A Yinzhuang Yi %A Jorge Cortes %A Nikolay Atanasov %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-long23a %I PMLR %P 864--877 %U https://proceedings.mlr.press/v211/long23a.html %V 211 %X This paper develops methods for proving Lyapunov stability of dynamical systems subject to disturbances with an unknown distribution. We assume only a finite set of disturbance samples is available and that the true online disturbance realization may be drawn from a different distribution than the given samples. We formulate an optimization problem to search for a sum-of-squares (SOS) Lyapunov function and introduce a distributionally robust version of the Lyapunov function derivative constraint. We show that this constraint may be reformulated as several SOS constraints, ensuring that the search for a Lyapunov function remains in the class of SOS polynomial optimization problems. For general systems, we provide a distributionally robust chance-constrained formulation for neural network Lyapunov function search. Simulations demonstrate the validity and efficiency of either formulation on non-linear uncertain dynamical systems.
APA
Long, K., Yi, Y., Cortes, J. & Atanasov, N.. (2023). Distributionally Robust Lyapunov Function Search Under Uncertainty. Proceedings of The 5th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 211:864-877 Available from https://proceedings.mlr.press/v211/long23a.html.

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