可到達集合の凸包
Convex Hulls of Reachable Sets
有界外乱と不確かな初期条件をもつ非線形システムの可到達集合の凸包を、球面上の初期条件をもつ常微分方程式の解の凸包として特徴づけ、効率的なサンプリングベースの過近似推定アルゴリズムを提案した。
著者: Thomas Lew, Riccardo Bonalli, Marco Pavone
分類: math.OC, cs.LG, cs.RO, cs.SY, eess.SY
原文アブストラクト
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.
