  Artificial neural networks have recently been utilized in many feedback
control systems and introduced new challenges regarding the safety of such
systems. This paper considers the safe verification problem for a dynamical
system with a given feedforward neural network as the feedback controller by
using a constrained zonotope-based approach. A novel set-based method is
proposed to compute both exact and over-approximated reachable sets for neural
feedback systems with linear models, and linear program-based sufficient
conditions are presented to verify whether the trajectories of such a system
can avoid unsafe regions represented as constrained zonotopes. The results are
also extended to neural feedback systems with nonlinear models. The
computational efficiency and accuracy of the proposed method are demonstrated
by two numerical examples where a comparison with state-of-the-art methods is
also provided.
