Forward Stochastic Reachability Analysis for Uncontrolled Linear Systems using Fourier Transforms
Provides exact analytical solutions for stochastic reachability in linear systems, benefiting control and robotics applications where precise probability computations are needed.
The paper introduces a Fourier transform-based method for exact forward stochastic reachability analysis in uncontrolled linear systems with affine disturbance, providing analytical expressions for reach probability densities and sets. Demonstrated on robot-target capture examples, it outperforms traditional approximation methods.
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.