Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Distributionally robust policy and
Lyapunov-certificate learning
K. Long, J. Cortés,
N. Atanasov
IEEE Open Journal of Control Systems, submitted
Abstract
This article presents novel methods for synthesizing
distributionally robust stabilizing neural
controllers and certificates for control systems
under model uncertainty. A key challenge in
designing controllers with stability guarantees for
uncertain systems is the accurate determination of
and adaptation to shifts in model parametric
uncertainty during online deployment. We tackle this
with a novel distributionally robust formulation of
the Lyapunov derivative chance constraint ensuring a
monotonic decrease of the Lyapunov certificate. To
avoid the computational complexity involved in
dealing with the space of probability measures, we
identify a sufficient condition in the form of
deterministic convex constraints that ensures the
Lyapunov derivative constraint is satisfied. We
integrate this condition into a loss function for
training a neural network-based controller and show
that, for the resulting closed-loop system, the
global asymptotic stability of its equilibrium can
be certified with high confidence, even with
Out-of-Distribution (OoD) model uncertainties. To
demonstrate the efficacy and efficiency of the
proposed methodology, we compare it with an
uncertainty-agnostic baseline approach and several
reinforcement learning approaches in two control
problems in simulation. Open-source implementations
of the examples are available at
https://github.com/KehanLong/DR Stabilizing Policy.
pdf
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