This package implements numerical solvers for Hamilton-Jacobi (HJ) Partial Differential Equations (PDEs) which, in the context of optimal control, may be used to represent the continuous-time formulation of dynamic programming. Specifically, the focus of this package is on reachability analysis for zero-sum differential games modeled as Hamilton-Jacobi-Isaacs (HJI) PDEs, wherein an optimal controller and (optional) disturbance interact, and the set of reachable states at any time is represented as the zero sublevel set of a value function realized as the viscosity solution of the corresponding PDE.

This package is inspired by a number of related projects, including:

• A Toolbox of Level Set Methods (toolboxls, MATLAB)
• An Optimal Control Toolbox for Hamilton-Jacobi Reachability Analysis (helperOC, MATLAB)
• Berkeley Efficient API in C++ for Level Set methods (beacls, C++/CUDA C++)
• Optimizing Dynamic Programming-Based Algorithms (optimized_dp, python)

To accommodate different JAX versions (i.e., CPU-only vs. JAX with GPU support), this package does not list JAX as a dependency in requirements.txt. Therefore, to use this package you must first install JAX (with your preferred accelerator support); see the JAX installation instructions for details.

Then, install this package using pip:

pip install --upgrade hj-reachability

Aside from the specific TODOs scattered throughout the codebase, a few general TODOs:

• Single-line docstrings (at a bare minimum) for everything. Test coverage, book/paper references, and proper documentation to come... eventually.
• Look into using jax.pmap/jax.lax.ppermute for multi-device parallelism; see, e.g., jax demo notebooks.
• Incorporate neural-network-based PDE solvers; see, e.g., Bansal, S. and Tomlin, C. "DeepReach: A Deep Learning Approach to High-Dimensional Reachability." (2020).