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Sampling-based Reachability Analysis A Random Set Theory Approach with Adversarial Sampling

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Document pages: 16 pages

Abstract: Reachability analysis is at the core of many applications, from neuralnetwork verification, to safe trajectory planning of uncertain systems.However, this problem is notoriously challenging, and current approaches tendto be either too restrictive, too slow, too conservative, or approximate andtherefore lack guarantees. In this paper, we propose a simple yet effectivesampling-based approach to perform reachability analysis for arbitrarydynamical systems. Our key novel idea consists of using random set theory togive a rigorous interpretation of our method, and prove that it returns setswhich are guaranteed to converge to the convex hull of the true reachable sets.Additionally, we leverage recent work on robust deep learning and propose a newadversarial sampling approach to robustify our algorithm and accelerate itsconvergence. We demonstrate that our method is faster and less conservativethan prior work, present results for approximate reachability analysis ofneural networks and robust trajectory optimization of high-dimensionaluncertain nonlinear systems, and discuss future applications.

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