利用傅里叶变换的未受控线性系统前向随机可达性分析
Forward Stochastic Reachability Analysis for Uncontrolled Linear Systems using Fourier Transforms
AI总结：
本文提出一种可扩展方法，利用傅里叶变换高效计算未受控线性系统前向随机可达概率测度（密度）和可达集，适用于有界或无界的扰动集，并探讨了可达集的凸性性质。
摘要：
我们提出了一种可扩展的方法，用于未受控线性系统在具有仿射扰动下的前向随机可达性分析。我们的方法利用傅里叶变换高效计算前向随机可达概率测度（密度）和前向随机可达集。该方法适用于具有有界或无界扰动集的系统。我们还研究了前向随机可达集及其概率密度的凸性性质。受机器人试图捕捉随机移动、非对抗性目标问题的启发，我们在两个简单例子上展示了我们的方法。传统方法提供近似值，而我们的方法提供精确的解析表达式，用于密度和捕捉概率。
英文摘要：
We propose a scalable method for forward stochastic reachability analysis for uncontrolled linear systems with affine disturbance. Our method uses Fourier transforms to efficiently compute the forward stochastic reach probability measure (density) and the forward stochastic reach set. This method is applicable to systems with bounded or unbounded disturbance sets. We also examine the convexity properties of the forward stochastic reach set and its probability density. Motivated by the problem of a robot attempting to capture a stochastically moving, non-adversarial target, we demonstrate our method on two simple examples. Where traditional approaches provide approximations, our method provides exact analytical expressions for the densities and probability of capture.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
