%AMiller, Jared%ASznaier, Mario%BJournal Name: IEEE Transactions on Automatic Control
%D2023%I
%JJournal Name: IEEE Transactions on Automatic Control
%K
%MOSTI ID: 10447854
%PMedium: X
%TBounding the Distance to Unsafe Sets With Convex Optimization
%XThis work proposes an algorithm to bound the minimum distance between points on trajectories of a dynamical system and points on an unsafe set. Prior work on certifying safety of trajectories includes barrier and density methods, which do not provide a margin of proximity to the unsafe set in terms of distance. The distance estimation problem is relaxed to a Monge-Kantorovich-type optimal transport problem based on existing occupation-measure methods of peak estimation. Specialized programs may be developed for polyhedral norm distances (e.g. L1 and Linfinity) and for scenarios where a shape is traveling along trajectories (e.g. rigid body motion). The distance estimation problem will be correlatively sparse when the distance objective is separable.
%0Journal Article