Scalable Underapproximation for the Stochastic Reach-Avoid Problem for High-Dimensional LTI Systems using Fourier Transforms
From MaRDI portal
Publication:6283977
arXiv1703.02135MaRDI QIDQ6283977
Author name not available (Why is that?)
Publication date: 6 March 2017
Abstract: We present a scalable underapproximation of the terminal hitting time stochastic reach-avoid probability at a given initial condition, for verification of high-dimensional stochastic LTI systems. While several approximation techniques have been proposed to alleviate the curse of dimensionality associated with dynamic programming, these techniques are limited and cannot handle larger, more realistic systems. We present a scalable method that uses Fourier transforms to compute an underapproximation of the reach-avoid probability for systems with disturbances with arbitrary probability densities. We characterize sufficient conditions for Borel-measurability of the value functions. We exploit fixed control sequences parameterized by the initial condition (an open-loop control policy) to generate the underapproximation. For Gaussian disturbances, the underapproximation can be obtained using existing efficient algorithms by solving a convex optimization problem. Our approach produces non-trivial lower bounds and is demonstrated on a chain of integrators with 40 states.
No records found.
This page was built for publication: Scalable Underapproximation for the Stochastic Reach-Avoid Problem for High-Dimensional LTI Systems using Fourier Transforms
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6283977)
