Artificial neural networks (ANNs) have been utilized in many feedback control
systems and introduced new challenges regarding the safety of the system. This
paper considers the problem of verifying whether the trajectories of a system
with a feedforward neural network (FNN) controller can avoid unsafe regions,
using a constrained zonotope-based reachability analysis approach. FNNs with
the rectified linear unit activation function are considered in this work. A
novel set-based method is proposed to compute both exact and over-approximated
reachable sets for linear discrete-time systems with FNN controllers, and
linear program-based sufficient conditions are presented to certify the safety
of the neural feedback systems. Reachability analysis and safety verification
for neural feedback systems with nonlinear models are also considered. 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.Comment: 8 pages, 4 figure