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 over-approximation 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 over-approximate 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 MPC.

翻译：本文研究了具有有界扰动和不确定初始条件的非线性系统可达集的凸包。可达集在控制领域中扮演着关键角色，但其计算一直极具挑战性，现有的过近似工具往往趋于保守或计算成本高昂。本工作将可达集的凸包刻画为一个初始条件位于球面上的常微分方程解的凸包。这一有限维刻画启发出一种高效的基于采样的估计算法，用于精确过近似可达集。我们还研究了可达凸包边界结构，并推导了估计算法的误差界。最后，我们给出了在神经反馈环路分析和鲁棒模型预测控制中的应用。