We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances. 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 exactly characterize the convex hulls of reachable sets as the convex hulls of solutions of an ordinary differential equation from all possible initial values of the disturbances. This finite-dimensional characterization unlocks a fast sampling-based method to accurately over-approximate reachable sets. We give applications to neural feedback loop analysis and robust model predictive control.

翻译：我们研究了带界扰动非线性系统可达集凸包的问题。可达集在控制领域具有关键作用，但其计算历来极具挑战性，而现有的过逼近工具往往过于保守或计算成本高昂。本文中，我们精确地将可达集凸包表征为从所有可能的扰动初始值出发的常微分方程解的凸包。这种有限维刻画为基于快速采样的方法提供了可能，从而实现对可达集的精确过逼近。我们给出了该方法在神经反馈回路分析与鲁棒模型预测控制中的应用。