  Deep neural classifiers have recently found tremendous success in data-driven
control systems. However, existing models suffer from a trade-off between
accuracy and adversarial robustness. This limitation must be overcome in the
control of safety-critical systems that require both high performance and
rigorous robustness guarantees. In this work, we develop classifiers that
simultaneously inherit high robustness from robust models and high accuracy
from standard models. Specifically, we propose a theoretically motivated
formulation that mixes the output probabilities of a standard neural network
and a robust neural network. Both base classifiers are pre-trained, and thus
our method does not require additional training. Our numerical experiments
verify that the mixed classifier noticeably improves the accuracy-robustness
trade-off and identify the confidence property of the robust base classifier as
the key leverage of this more benign trade-off. Our theoretical results prove
that under mild assumptions, when the robustness of the robust base model is
certifiable, no alteration or attack within a closed-form $\ell_p$ radius on an
input can result in the misclassification of the mixed classifier.
