Forward Stochastic Reachability Analysis for Uncontrolled Linear Systems using Fourier Transforms
Forward Stochastic Reachability Analysis for Uncontrolled Linear Systems using Fourier Transforms
复制标题
使用傅立叶变换对不受控线性系统进行正向随机可达性分析
DOI：
10.1145/3049797.3049818
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Meeko Oishi
中科院分区：
文献类型：
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作者：
Abraham P. Vinod;B. Homchaudhuri;Meeko Oishi
提出了一种可扩展的仿射扰动不可控线性系统前向随机可达性分析方法。我们的方法使用傅立叶变换来有效地计算前向随机到达概率测度（密度）和前向随机到达集。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。出于这个问题的机器人试图捕捉一个随机移动，非对抗性的目标，我们证明了我们的方法在两个简单的例子。传统的方法提供近似，我们的方法提供了精确的解析表达式的密度和捕获的概率。
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.