Bounding the Distance to Unsafe Sets With Convex Optimization

• 成果类型: Article
• 署名作者: Miller, Jared; Sznaier, Mario
• 署名单位: Northeastern University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3285862
• 发表日期: 2023
• 页码: 7575-7590
• 关键词: Linear matrix inequality (LMI); numerical optimization; peak estimation; safety; sum of squares (SOS)

摘要

This work proposes an algorithm to bind 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.