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
@article{arxiv.2212.01554,
title = {Distributionally Robust Lyapunov Function Search Under Uncertainty},
author = {Kehan Long and Yinzhuang Yi and Jorge Cortes and Nikolay Atanasov},
journal= {arXiv preprint arXiv:2212.01554},
year = {2024}
}
Comments
5th Annual Learning for Dynamics & Control Conference Code: https://github.com/KehanLong/DR-Lyapunov-Function