Unbounded-Time Safety Verification of Stochastic Differential Dynamics release_rnht75insbdtvm52rvmoztmvqe

by Shenghua Feng, Mingshuai Chen, Bai Xue, Sriram Sankaranarayanan, Naijun Zhan

Released as a article .

2020  

Abstract

In this paper, we propose a method for bounding the probability that a stochastic differential equation (SDE) system violates a safety specification over the infinite time horizon. SDEs are mathematical models of stochastic processes that capture how states evolve continuously in time. They are widely used in numerous applications such as engineered systems (e.g., modeling how pedestrians move in an intersection), computational finance (e.g., modeling stock option prices), and ecological processes (e.g., population change over time). Previously the safety verification problem has been tackled over finite and infinite time horizons using a diverse set of approaches. The approach in this paper attempts to connect the two views by first identifying a finite time bound, beyond which the probability of a safety violation can be bounded by a negligibly small number. This is achieved by discovering an exponential barrier certificate that proves exponentially converging bounds on the probability of safety violations over time. Once the finite time interval is found, a finite-time verification approach is used to bound the probability of violation over this interval. We demonstrate our approach over a collection of interesting examples from the literature, wherein our approach can be used to find tight bounds on the violation probability of safety properties over the infinite time horizon.
In text/plain format

Archived Files and Locations

application/pdf  603.3 kB
file_ox3yd3qul5adrdpqlz3vb54zwa
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2020-06-02
Version   v1
Language   en ?
arXiv  2006.01858v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 305bd071-38dd-4902-be37-1a7b912cf2a4
API URL: JSON