Year: 2021
Type: preprint
Abstract: In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of dynamical systems. By sampling inputs, evaluating their images in the true reachable set, and taking their $ε$-padded convex hull as a set estimator, this algorithm applies to general problem settings and is simple to implement. Our main contribution is the derivation of asymptotic and finite-sample accuracy guarantees using random set theory. This analysis informs algorithmic design to obtain an $ε$-close reachable set approximation with high probability, provides insights into which reachability problems are most challenging, and motivates safety-critical applications of the technique. On a neural network verification task, we show that this approach is more accurate and significantly faster than prior work. Informed by our analysis, we also design a robust model predictive controller that we demonstrate in hardware experiments.
Source: arXiv (Cornell University)
Institutions: Vaughn College of Aeronautics and Technology, American Institute of Aeronautics and Astronautics, Stanford University, Nanjing University of Aeronautics and Astronautics, Harvard University, Centre National de la Recherche Scientifique, Université Paris-Saclay, Laboratoire des signaux et systèmes, CentraleSupélec
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4200628918