{"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/a-barrier-function-approach-to-finite-time","title":"A Barrier Function Approach to Finite-Time Stochastic System Verification and Control","arxiv_id":"1909.05109","date":"2019-09-10","proceeding":null,"authors":[],"abstract":"This paper studies the problem of enforcing safety of a stochastic dynamical\nsystem over a finite-time horizon. We use stochastic control barrier functions\nas a means to quantify the probability that a system exits a given safe region\nof the state space in finite time. A barrier certificate condition that bounds\nthe expected value of the barrier function over the time horizon is recast as a\nsum-of-squares optimization problem for efficient numerical computation. Unlike\nprior works, the proposed certificate condition includes a state-dependent\nupper bound on the evolution of the expectation. We present formulations for\nboth continuous-time and discrete-time systems. Moreover, for systems for which\nthe drift dynamics are affine-in-control, we propose a method for synthesizing\npolynomial state feedback controllers that achieve a specified probability of\nsafety. Several case studies are presented which benchmark and illustrate the\nperformance of our verification and control method in the continuous-time and\ndiscrete-time domains.","url_abs":"http://arxiv.org/abs/1909.05109v1","url_pdf":"http://arxiv.org/pdf/1909.05109v1.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":"abstracts"},"code_links":[{"paper_slug":"a-barrier-function-approach-to-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":{"syntology_url":"https://syntology.ai/paper/1909.05109","atlas_url":"https://app.syntology.ai/?focus=1909.05109","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}