  In this paper, we present a data-driven framework for real-time estimation of
reachable sets for control systems where the plant is modeled using neural
networks (NNs). We utilize a running example of a quadrotor model that is
learned using trajectory data via NNs. The NN learned offline, can be excited
online to obtain linear approximations for reachability analysis. We use a
dynamic mode decomposition based approach to obtain linear liftings of the NN
model. The linear models thus obtained can utilize optimal control theory to
obtain polytopic approximations to the reachable sets in real-time. The
polytopic approximations can be tuned to arbitrary degrees of accuracy. The
proposed framework can be extended to other nonlinear models that utilize NNs
to estimate plant dynamics. We demonstrate the effectiveness of the proposed
framework using an illustrative simulation of quadrotor dynamics.
