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Title: Bounding the Distance to Unsafe Sets With Convex Optimization
This 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.  more » « less
Award ID(s):
2208182 2038493
Author(s) / Creator(s):
Date Published:
Journal Name:
IEEE Transactions on Automatic Control
Page Range / eLocation ID:
1 to 15
Medium: X
Sponsoring Org:
National Science Foundation
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