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：我们研究带有有界扰动的非线性系统可达集的凸壳。可达集在控制领域发挥关键作用，但其计算历来极具挑战性，现有过逼近工具往往过于保守或计算成本高昂。本研究精确刻画了可达集的凸壳，将其表述为所有可能扰动初值下常微分方程解的凸壳。这一有限维刻画使得一种紧致估计算法得以实现，该算法能够以显著高于现有方法的速度和精度对可达集进行过逼近。我们展示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。