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Title: Bounding the Distance of Closest Approach to Unsafe Sets with Occupation Measures
This paper presents a method to lower-bound the distance of closest approach between points on an unsafe set and points along system trajectories. Such a minimal distance is a quantifiable and interpretable certificate of safety of trajectories, as compared to prior art in barrier and density methods which offers a binary indication of safety/unsafety. The distance estimation problem is converted into a infinitedimensional linear program in occupation measures based on existing work in peak estimation and optimal transport. The moment-SOS hierarchy is used to obtain a sequence of lower bounds obtained through solving semidefinite programs in increasing size, and these lower bounds will converge to the true minimal distance as the degree approaches infinity under mild conditions (e.g. Lipschitz dynamics, compact sets).  more » « less
Award ID(s):
2208182 1808381
Author(s) / Creator(s):
Date Published:
Journal Name:
60th IEEE Conf. Decision and Control
Page Range / eLocation ID:
5008- 5013
Medium: X
Sponsoring Org:
National Science Foundation
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