  Hamilton-Jacobi (HJ) reachability analysis is an important formal
verification method for guaranteeing performance and safety properties of
dynamical systems; it has been applied to many small-scale systems in the past
decade. Its advantages include compatibility with general nonlinear system
dynamics, formal treatment of bounded disturbances, and the availability of
well-developed numerical tools. The main challenge is addressing its
exponential computational complexity with respect to the number of state
variables. In this tutorial, we present an overview of basic HJ reachability
theory and provide instructions for using the most recent numerical tools,
including an efficient GPU-parallelized implementation of a Level Set Toolbox
for computing reachable sets. In addition, we review some of the current work
in high-dimensional HJ reachability to show how the dimensionality challenge
can be alleviated via various general theoretical and application-specific
insights.
