Distributionally Robust Lyapunov Function Search Under Uncertainty
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
Text
Long et al. "Distributionally Robust Lyapunov Function Search Under Uncertainty." Proceedings of The 5th Annual Learning for Dynamics and Control Conference, 2023.Markdown
[Long et al. "Distributionally Robust Lyapunov Function Search Under Uncertainty." Proceedings of The 5th Annual Learning for Dynamics and Control Conference, 2023.](https://mlanthology.org/l4dc/2023/long2023l4dc-distributionally/)BibTeX
@inproceedings{long2023l4dc-distributionally,
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},
year = {2023},
pages = {864-877},
volume = {211},
url = {https://mlanthology.org/l4dc/2023/long2023l4dc-distributionally/}
}