{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,3]],"date-time":"2026-05-03T05:44:20Z","timestamp":1777787060592,"version":"3.51.4"},"reference-count":38,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"5","license":[{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2023YFA1009402"],"award-info":[{"award-number":["2023YFA1009402"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62472362"],"award-info":[{"award-number":["62472362"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62272397"],"award-info":[{"award-number":["62272397"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171159"],"award-info":[{"award-number":["12171159"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["40500-20104-222609"],"award-info":[{"award-number":["40500-20104-222609"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst."],"published-print":{"date-parts":[[2026,5]]},"DOI":"10.1109\/tcad.2025.3616856","type":"journal-article","created":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T17:39:18Z","timestamp":1759340358000},"page":"2460-2473","source":"Crossref","is-referenced-by-count":0,"title":["Safe Reinforcement Learning for NN-Controlled Systems With Neural Barrier Certificate Guidance"],"prefix":"10.1109","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5246-0330","authenticated-orcid":false,"given":"Hanrui","family":"Zhao","sequence":"first","affiliation":[{"name":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-3772-8369","authenticated-orcid":false,"given":"Mengxin","family":"Ren","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-3584-1339","authenticated-orcid":false,"given":"Banglong","family":"Liu","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-5352-3681","authenticated-orcid":false,"given":"Niuniu","family":"Qi","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2575-7045","authenticated-orcid":false,"given":"Xia","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Computer and Information Science, Southwest University, Chongqing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9728-1114","authenticated-orcid":false,"given":"Zhenbing","family":"Zeng","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1209-8191","authenticated-orcid":false,"given":"Zhengfeng","family":"Yang","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/CCTA.2018.8511342"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1145\/3705307"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2010.5717115"},{"key":"ref4","article-title":"Continuous control with deep reinforcement learning","author":"Lillicrap","year":"2015","journal-title":"arXiv:1509.02971"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-24743-2_32"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/ICCAD45719.2019.8942130"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1145\/1995376.1995394"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s00165-021-00544-5"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/CCTA49430.2022.9966192"},{"key":"ref10","first-page":"95","article-title":"Formally verifying deep reinforcement learning controllers with Lyapunov barrier certificates","volume-title":"Proc. FMCAD","author":"Mandal"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/DAC18074.2021.9586327"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-81685-8_22"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-39799-8_17"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.23919\/ECC.2019.8796030"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/SMC.2017.8122622"},{"key":"ref16","first-page":"11423","article-title":"Efficient and accurate estimation of Lipschitz constants for deep neural networks","volume-title":"Proc. NeurIPS","author":"Fazlyab"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1145\/3641513.3651398"},{"key":"ref18","first-page":"698","article-title":"On the expressive power of deep learning: A tensor analysis","volume-title":"Proc. Conf. Learn. Theory","author":"Cohen"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1145\/3447928.3456646"},{"issue":"2","key":"ref21","first-page":"62","article-title":"Linear matrix inequalities in control","volume":"3","author":"Scherer","year":"2000","journal-title":"Lect. Notes"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1993.42.42045"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3216-0_8"},{"key":"ref24","first-page":"1","article-title":"Neural barrier certificates synthesis of NN-controlled continuous systems via counterexample-guided learning","volume-title":"Proc. 61st ACM\/IEEE Design Autom. Conf.","author":"Zhao"},{"key":"ref25","volume-title":"Penbmi User\u2019s Guide","author":"Kocvara","year":"2005"},{"key":"ref26","volume-title":"SOSTOOLS: Sum of Squares Optimization Toolbox for MATLAB","author":"Prajna","year":"2004"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1080\/09540091.2022.2151567"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2004.835589"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-53288-8_29"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1145\/2968478.2968484"},{"key":"ref31","article-title":"Stabilization of polynomial dynamical systems using linear programming based on Bernstein polynomials","author":"Sassi","year":"2015","journal-title":"arXiv:1501.04578"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1002\/3527603603"},{"key":"ref33","volume-title":"Quadcopter Model","author":"Gao","year":"2016"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1109\/DAC56929.2023.10247837"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-37706-8_16"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2007.902736"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1145\/3365365.3382222"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1145\/3609125"}],"container-title":["IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/43\/11493579\/11187424.pdf?arnumber=11187424","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T19:49:18Z","timestamp":1777492158000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/11187424\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5]]},"references-count":38,"journal-issue":{"issue":"5"},"URL":"https:\/\/doi.org\/10.1109\/tcad.2025.3616856","relation":{},"ISSN":["0278-0070","1937-4151"],"issn-type":[{"value":"0278-0070","type":"print"},{"value":"1937-4151","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5]]}}}