基于采样的随机模型预测控制中退出泛函的高阶逼近

中文摘要 AI 辅助

在基于采样的随机模型预测控制中，安全性评估通常需要对退出泛函进行数值估计。因此，首次退出时间和退出指标的逼近是一个关键的数值瓶颈，这些量的离散化误差直接影响最终的控制性能。本文研究了如何将现有的高阶强逼近方法引入安全控制中。文中重点讨论两种情况：对于一般的非交换动力学，采用自适应一阶Milstein离散化，并结合Wiktorsson方法进行Lévy面积模拟；对于交换动力学，自适应1.5阶构造实现了更强的退出时间收敛速率。在退出时间分布的局部反集中条件下，我们证明了强退出时间逼近可以传递为失效指标的强逼近。随后，这些方法在机会约束路径积分控制的背景下进行研究，该控制通过退出事件提供了安全性的精确连续时间表示。数值实验比较了两种情况在强退出时间误差、失效指标误差和闭环约束满足度方面的表现，结果显示相对于Euler-Maruyama方法有显著改进，从而支持了现有及未来依赖于改进强逼近技术的应用。

英文摘要

Safety evaluation in sampling-based stochastic model predictive control often requires numerical estimation of exit functionals. The approximation of first-exit times and exit indicators is therefore a key numerical bottleneck, and discretization error in these quantities directly affects the resulting controller. This paper studies how existing higher-order methods for strong approximation of exit times can be brought into safe control. Two cases are highlighted. For general noncommutative dynamics, an adaptive order-1 Milstein discretization is used together with Lévy-area simulation via Wiktorsson's method. For commutative dynamics, an adaptive order-1.5 construction achieves a stronger exit-time rate. Under a local anti-concentration condition on the exit-time law, we show that strong exit-time approximation transfers to strong approximation of the failure indicator. The methods are then studied in the context of chance-constrained path integral control, which provides an exact continuous-time representation of safety through exit events. Numerical experiments compare the two cases in terms of strong exit-time error, failure-indicator error, and closed-loop constraint satisfaction, showing improvement over Euler-Maruyama and thereby enabling existing and future techniques whose applicability depends on improved strong approximation.

发表机构

• Purdue University（普渡大学）

机构由 AI 辅助整理，请以论文原文为准。

补充信息

备注

Accepted for publication in the proceedings of the 2026 IEEE Conference on Decision and Control (CDC 2026)