  Deep neural networks can be trained to be efficient and effective controllers
for dynamical systems; however, the mechanics of deep neural networks are
complex and difficult to guarantee. This work presents a general approach for
providing guarantees for deep neural network controllers over multiple time
steps using a combination of reachability methods and open source neural
network verification tools. By bounding the system dynamics and neural network
outputs, the set of reachable states can be over-approximated to provide a
guarantee that the system will never reach states outside the set. The method
is demonstrated on the mountain car problem as well as an aircraft collision
avoidance problem. Results show that this approach can provide neural network
guarantees given a bounded dynamic model.
