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 tight estimation algorithm to over-approximate reachable sets that is significantly faster and more accurate than existing methods. We present applications to neural feedback loop analysis and robust model predictive control.

翻译：本文研究具有有界扰动的非线性系统可达集的凸包。可达集在控制中扮演着关键角色，但计算仍具有挑战性，现有的超逼近工具往往保守或计算成本高。在本文中，我们准确地将可达集的凸包表征为从扰动的所有可能的初始值开始的普通微分方程的解的凸包。这种有限维度的表征解锁了一种紧凑的估计算法来超逼近可达集，该算法比现有方法更快速和更准确。我们提供了神经反馈回路分析和鲁棒模型预测控制的应用。