Estimating Reachable Sets with Scenario Optimization
Estimating Reachable Sets with Scenario Optimization
复制标题
DOI：
--
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Alex Devonport;M. Arcak
中科院分区：
文献类型：
--
作者：
Alex Devonport;M. Arcak
许多实际系统不服从可达性方法，保证正确性，因为它们具有强非线性，不确定性，可能是未知的动态。虽然这类系统的可达集仍然可以用数据驱动的方式来估计，但数据驱动的方法通常不能保证其结果的有效性。然而，某些数据驱动的方法可以通过将问题重构为利用场景优化来解决的机会约束优化问题来给出正确性的概率保证。我们将这种方法应用于通过数据的范球来逼近可达集的问题。该方法只需要O（n2）的样本轨迹和凸问题的解决方案。该方法的一个变体仅限于轴对齐的范数球，只需要O（n）个样本。
Many practical systems are not amenable to the reachability methods that give guarantees of correctness, since they have dynamics that are strongly nonlinear, uncertain, and possibly unknown. While reachable sets for these kinds of systems can still be estimated in a data-driven way, data-driven methods typically do not guarantee the validity of their results. However, certain data-driven approaches may be given a probabilistic guarantee of correctness, by reframing the problem as a chance-constrained optimization problem that is solved with scenario optimization. We apply this approach to the problem of approximating a reachable set by a norm ball from data. The method requires only O ( n 2 ) sample trajectories and the solution of a convex problem. A variant of the method restricted to axis-aligned norm balls requires only O ( n ) samples.