{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/verification-and-control-for-finite-time","title":"Verification and Control for Finite-Time Safety of Stochastic Systems via Barrier Functions","arxiv_id":"1905.12077","date":"2019-05-28","proceeding":null,"authors":["Cesar Santoyo","Maxence Dutreix","Samuel Coogan"],"abstract":"This paper studies the problem of enforcing safety of a stochastic dynamical system over a finite time horizon. We use stochastic barrier functions as a means to quantify the probability that a system exits a given safe region of the state space in finite time. A barrier certificate condition that bounds the infinitesimal generator of the system, and hence bounds the expected value of the barrier function over the time horizon, is recast as a sum-of-squares optimization problem for efficient numerical computation. Unlike prior works, the proposed certificate condition includes a state-dependent bound on the infinitesimal generator, allowing for tighter probability bounds. Moreover, for stochastic systems for which the drift dynamics are affine-in-control, we propose a method for synthesizing polynomial state feedback controllers that achieve a specified probability of safety. Two case studies are presented that benchmark and illustrate the performance of our method.","url_abs":"http://arxiv.org/abs/1905.12077v1","url_pdf":"http://arxiv.org/pdf/1905.12077v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"verification-and-control-for-finite-time","repo_url":"https://github.com/gtfactslab/stochasticbarrierfunctions","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}