  Learning-based methods could provide solutions to many of the long-standing
challenges in control. However, the neural networks (NNs) commonly used in
modern learning approaches present substantial challenges for analyzing the
resulting control systems' safety properties. Fortunately, a new body of
literature could provide tractable methods for analysis and verification of
these high dimensional, highly nonlinear representations. This tutorial first
introduces and unifies recent techniques (many of which originated in the
computer vision and machine learning communities) for verifying robustness
properties of NNs. The techniques are then extended to provide formal
guarantees of neural feedback loops (e.g., closed-loop system with NN control
policy). The provided tools are shown to enable closed-loop reachability
analysis and robust deep reinforcement learning.
