Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Distributionally robust Lyapunov function search under uncertainty
K. Long, Y. Yi, J. Cortés, N. Atanasov
Conference on Learning for Dynamics and
Control, Philadelphia, Pennsylvania, 2023,
Proceedings of Machine Learning Research,
volume 211, pp. 864-877
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.
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Mechanical and Aerospace Engineering,
University of California, San Diego
9500 Gilman Dr,
La Jolla, California, 92093-0411
Ph: 1-858-822-7930
Fax: 1-858-822-3107
cortes at ucsd.edu
Skype id:
jorgilliyo