Sample-Based Methods for Reachability, Invariance, and Safety

Abstract

Reachable and invariant sets are essential ingredients for control and safety verification of autonomous systems, but classical methods struggle to scale to complex, high-dimensional models. This talk presents a suite of sample-based methods for computing reachable and controlled invariant sets with probabilistic guarantees. First, we use ideas from scenario optimization and statistical learning to construct reachable set approximations from sampled trajectories and certify their generalization to unsampled ones. Next, we turn to Gaussian Process state-space models—which provide a principled way to combine prior models with data—and show how they can be used to compute probabilistic controlled invariant sets. Finally, we present a post hoc safety certification method based on importance sampling, enabling sample-efficient estimation of rare failure probabilities for candidate safe sets.

Biography

Murat Arcak is a professor at the University of California, Berkeley, where he holds the Robert M. Saunders Endowed Chair. He has a primary appointment in Electrical Engineering and Computer Sciences, and a courtesy appointment in Mechanical Engineering. He earned his B.S. degree in Electrical Engineering from Boğaziçi University, Istanbul, Turkey, in 1996, and his M.S. and Ph.D. degrees from the University of California, Santa Barbara, in 1997 and 2000. His research focuses on dynamical systems and control theory, with applications to autonomous and multiagent systems.