Convex Hulls of Reachable Sets
成果类型：
Article
署名作者：
Lew, Thomas; Bonalli, Riccardo; Pavone, Marco
署名单位：
Toyota Motor Corporation; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Stanford University
刊物名称：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN/ISSBN：
0018-9286
DOI：
10.1109/TAC.2025.3586777
发表日期：
2025
关键词：
摘要：
We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing overapproximation tools tend to be conservative or computationally expensive. In this work, we characterize the convex hulls of reachable sets as the convex hulls of solutions of an ordinary differential equation with initial conditions on the sphere. This finite-dimensional characterization unlocks an efficient sampling-based estimation algorithm to accurately overapproximate reachable sets. We also study the structure of the boundary of the reachable convex hulls and derive error bounds for the estimation algorithm. We give applications to neural feedback loop analysis and robust model predictive control.