  With the increase in data availability, it has been widely demonstrated that
neural networks (NN) can capture complex system dynamics precisely in a
data-driven manner. However, the architectural complexity and nonlinearity of
the NNs make it challenging to synthesize a provably safe controller. In this
work, we propose a novel safety filter that relies on convex optimization to
ensure safety for a NN system, subject to additive disturbances that are
capable of capturing modeling errors. Our approach leverages tools from NN
verification to over-approximate NN dynamics with a set of linear bounds,
followed by an application of robust linear MPC to search for controllers that
can guarantee robust constraint satisfaction. We demonstrate the efficacy of
the proposed framework numerically on a nonlinear pendulum system.
