Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Cautious optimization via data informativity
J. Eising, J. Cortés
Automatica, submitted
Abstract
This paper deals with the problem of accurately
determining guaranteed suboptimal values of an unknown cost function
on the basis of noisy measurements. We consider a set-valued variant
to regression where, instead of finding a best estimate of the cost
function, we reason over all functions compatible with the
measurements and apply robust methods explicitly in terms of the
data. Our treatment provides data-based conditions under which
closed-forms expressions of upper bounds of the unknown function can
be obtained, and regularity properties like convexity and
Lipschitzness can be established. These results allow us to provide
tests for point- and set-wise verification of suboptimality, and
tackle the cautious optimization of the unknown function in both
one-shot and online scenarios. We showcase the versatility of the
proposed methods in two control-relevant problems: data-driven
contraction analysis of unknown nonlinear systems and suboptimal
regulation with unknown dynamics and cost. Simulations illustrate our
results.
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
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jorgilliyo