Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances [article]

Somil Bansal, Mo Chen, Sylvia Herbert, Claire J. Tomlin
2017 arXiv   pre-print
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
more » ... er 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.
arXiv:1709.07523v1 fatcat:rsmzcy5dk5cl7n74cwwulgqhj4