矩不确定下有限时域安全性的最坏情况概率界
Worst-Case Probability Bounds for Finite-Horizon Safety under Moment Uncertainty
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中文总结 AI 辅助
本文针对初始状态矩不确定的动力系统，利用moment-SOS和SOS框架提出对偶规划方法，估计有限时域内进入非期望区域的最坏情况概率上界，经轨道物体等案例验证有效。
中文摘要 AI 辅助
本文研究估计动力系统在有限时域内某一时刻进入非期望区域的概率上界问题，不确定性的主要来源是系统初始状态，仅已知其有限组矩或处于规定区间内。为解决该问题，我们构建了基于测度的规划问题，并利用矩和平方和（moment-SOS）框架提出其松弛形式，对应的对偶问题被构造为泛函规划，随后被强化为平方和（SOS）规划。值得注意的是，该对偶形式与用于证明系统安全性的经典障碍函数技术具有结构相似性，关键区别在于它能产生概率性证明。通过多个案例研究验证了所提方法的有效性，包括一个涉及轨道上物体的案例。
英文摘要
This paper addresses the problem of estimating upper bounds on the probability that a dynamical system will enter an undesirable region at some point within a finite time horizon. The primary source of uncertainty lies in the system's initial state, for which only a finite set of moments is known or within a prescribed interval. To tackle this problem, we formulate a measure-based program and propose its relaxation using the moment-sum-of-squares (moment-SOS) framework. The corresponding dual problem is introduced as a functional program, which is subsequently strengthened into a sum-of-squares (SOS) program. Notably, this dual formulation bears a structural resemblance to classical barrier function techniques for certifying system safety, with the key distinction that it yields a probabilistic certificate. The effectiveness of the proposed approach is demonstrated through multiple case studies, including a case involving an object in orbit.
