PIRK: Scalable Interval Reachability Analysis for High-Dimensional Nonlinear Systems

Abstract: Reachability analysis is a critical tool for the formal verification of dynamical systems and the synthesis of controllers for them. Due to their computational complexity, many reachability analysis methods are restricted to systems with relatively small dimensions. One significant reason for such limitation is that those approaches, and their implementations, are not designed to leverage parallelism. They use algorithms that are designed to run serially within one compute unit and they can not utilize widely-available high-performance computing (HPC) platforms such as many-core CPUs, GPUs and Cloud-computing services. This paper presents PIRK, a tool to efficiently compute reachable sets for general nonlinear systems of extremely high dimensions. PIRK has been tested on several systems, with state dimensions ranging from ten up to 4 billion. The scalability of PIRK's parallel implementations is found to be highly favorable.