{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,2]],"date-time":"2026-11-02T08:28:29Z","timestamp":1793608109830,"version":"4.5.0"},"reference-count":31,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2027,2,1]],"date-time":"2027-02-01T00:00:00Z","timestamp":1801440000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2027,2,1]],"date-time":"2027-02-01T00:00:00Z","timestamp":1801440000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2027,2,1]],"date-time":"2027-02-01T00:00:00Z","timestamp":1801440000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2027,2,1]],"date-time":"2027-02-01T00:00:00Z","timestamp":1801440000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2027,2,1]],"date-time":"2027-02-01T00:00:00Z","timestamp":1801440000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2027,2,1]],"date-time":"2027-02-01T00:00:00Z","timestamp":1801440000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2027,2,1]],"date-time":"2027-02-01T00:00:00Z","timestamp":1801440000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100012576","name":"Guangdong Basic and Applied Basic Research Foundation","doi-asserted-by":"publisher","award":["2024A1515110109"],"award-info":[{"award-number":["2024A1515110109"]}],"id":[{"id":"10.13039\/501100012576","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62503093"],"award-info":[{"award-number":["62503093"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005047","name":"Natural Science Foundation of Liaoning Province","doi-asserted-by":"publisher","award":["2025-BS-0110"],"award-info":[{"award-number":["2025-BS-0110"]}],"id":[{"id":"10.13039\/501100005047","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["N25XQD038"],"award-info":[{"award-number":["N25XQD038"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["BX20250400"],"award-info":[{"award-number":["BX20250400"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100021171","name":"Basic and Applied Basic Research Foundation of Guangdong Province","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013804","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100013804","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Neural Networks"],"published-print":{"date-parts":[[2027,2]]},"DOI":"10.1016\/j.neunet.2026.109752","type":"journal-article","created":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T07:02:27Z","timestamp":1791874947000},"page":"109752","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"PA","title":["Lagrangian-based safe Q-learning for nonlinear delayed stochastic systems"],"prefix":"10.1016","volume":"206","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-4374-4013","authenticated-orcid":false,"given":"Kaidi","family":"Xing","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhongyang","family":"Ming","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiayue","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.neunet.2026.109752_bib0001","series-title":"2021 60th IEEE conference on decision and control (CDC)","first-page":"6829","article-title":"HJB based optimal safe control using control barrier functions","author":"Almubarak","year":"2021"},{"key":"10.1016\/j.neunet.2026.109752_bib0002","series-title":"2023 62nd IEEE conference on decision and control (CDC)","first-page":"241","article-title":"Safe Q-Learning for continuous-time linear systems","author":"Bandyopadhyay","year":"2023"},{"key":"10.1016\/j.neunet.2026.109752_bib0003","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2025.112458","article-title":"Lagrangian-based online safe reinforcement learning for state-constrained systems","volume":"179","author":"Bandyopadhyay","year":"2025","journal-title":"Automatica"},{"key":"10.1016\/j.neunet.2026.109752_bib0004","series-title":"Convex optimization","author":"Boyd","year":"2004"},{"key":"10.1016\/j.neunet.2026.109752_bib0005","doi-asserted-by":"crossref","DOI":"10.1016\/j.bspc.2021.102423","article-title":"Neural network-based physiological organ motion prediction and robot impedance control for teleoperated beating-heart surgery","volume":"66","author":"Cheng","year":"2021","journal-title":"Biomedical Signal Processing and Control"},{"key":"10.1016\/j.neunet.2026.109752_bib0006","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2022.110598","article-title":"Learning for MPC with stability & safety guarantees","volume":"146","author":"Gros","year":"2022","journal-title":"Automatica"},{"issue":"9","key":"10.1016\/j.neunet.2026.109752_bib0007","first-page":"3746","article-title":"Non-singular fixed-time tracking control of uncertain nonlinear pure-feedback systems with practical state constraints","volume":"70","author":"Guo","year":"2023","journal-title":"IEEE Transactions on Circuits and Systems I: Regular Papers"},{"issue":"3","key":"10.1016\/j.neunet.2026.109752_bib0008","doi-asserted-by":"crossref","first-page":"1722","DOI":"10.1109\/TSMC.2024.3515645","article-title":"Approximate dynamic programming for constrained piecewise affine systems with stability and safety guarantees","volume":"55","author":"He","year":"2025","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics: Systems"},{"issue":"11","key":"10.1016\/j.neunet.2026.109752_bib0009","doi-asserted-by":"crossref","first-page":"19023","DOI":"10.1109\/JIOT.2024.3364230","article-title":"State-of-the-art and future research challenges in UAV swarms","volume":"11","author":"Javed","year":"2024","journal-title":"IEEE Internet of Things Journal"},{"issue":"2","key":"10.1016\/j.neunet.2026.109752_bib0010","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1109\/TAC.2024.3441668","article-title":"Output feedback-based adaptive optimal output regulation for continuous-time strict-feedback nonlinear systems","volume":"70","author":"Jiang","year":"2025","journal-title":"IEEE Transactions on Automatic Control"},{"key":"10.1016\/j.neunet.2026.109752_bib0011","series-title":"Optimal control","author":"Lewis","year":"2012"},{"issue":"9","key":"10.1016\/j.neunet.2026.109752_bib0012","doi-asserted-by":"crossref","first-page":"5115","DOI":"10.1109\/TCYB.2024.3354945","article-title":"Dynamic event-triggered safe control for nonlinear game systems with asymmetric input saturation","volume":"54","author":"Liu","year":"2024","journal-title":"IEEE Transactions on Cybernetics"},{"issue":"4","key":"10.1016\/j.neunet.2026.109752_bib0013","doi-asserted-by":"crossref","first-page":"1932","DOI":"10.1109\/TNNLS.2021.3105681","article-title":"Event-triggered adaptive neural network control for stochastic nonlinear systems with state constraints and time-varying delays","volume":"34","author":"Liu","year":"2023","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"10.1016\/j.neunet.2026.109752_bib0014","doi-asserted-by":"crossref","first-page":"7082","DOI":"10.1002\/rnc.7334","article-title":"Safe adaptive output-feedback optimal control of a class of linear systems","volume":"34","author":"Mahmud","year":"2024","journal-title":"International Journal of Robust and Nonlinear Control"},{"issue":"5","key":"10.1016\/j.neunet.2026.109752_bib0015","doi-asserted-by":"crossref","first-page":"2743","DOI":"10.1109\/TAC.2022.3200948","article-title":"Safe value functions","volume":"68","author":"Massiani","year":"2023","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"1","key":"10.1016\/j.neunet.2026.109752_bib0016","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1109\/TASE.2022.3216733","article-title":"Mixed H2\/H\u221e control for nonlinear closed-loop Stackelberg games with application to power systems","volume":"21","author":"Ming","year":"2024","journal-title":"IEEE Transactions on Automation Science and Engineering"},{"issue":"12","key":"10.1016\/j.neunet.2026.109752_bib0017","doi-asserted-by":"crossref","first-page":"7804","DOI":"10.1109\/TCYB.2024.3403680","article-title":"Policy iteration Q-Learning for linear It\u00f4 stochastic systems with markovian jumps and its application to power systems","volume":"54","author":"Ming","year":"2024","journal-title":"IEEE Transactions on Cybernetics"},{"issue":"3","key":"10.1016\/j.neunet.2026.109752_bib0018","doi-asserted-by":"crossref","first-page":"1647","DOI":"10.1109\/TSMC.2024.3510594","article-title":"Self-triggered optimal control for unknown nonlinear random power systems with markovian switching","volume":"55","author":"Ming","year":"2025","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics: Systems"},{"issue":"2","key":"10.1016\/j.neunet.2026.109752_bib0019","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.1109\/LRA.2019.2897145","article-title":"Improved human\u2013robot collaborative control of redundant robot for teleoperated minimally invasive surgery","volume":"4","author":"Su","year":"2019","journal-title":"IEEE Robotics and Automation Letters"},{"issue":"12","key":"10.1016\/j.neunet.2026.109752_bib0020","doi-asserted-by":"crossref","first-page":"7933","DOI":"10.1109\/TCYB.2023.3240983","article-title":"Cooperative differential game-based distributed optimal synchronization control of heterogeneous nonlinear multiagent systems","volume":"53","author":"Sun","year":"2023","journal-title":"IEEE Transactions on Cybernetics"},{"issue":"4","key":"10.1016\/j.neunet.2026.109752_bib0021","doi-asserted-by":"crossref","first-page":"918","DOI":"10.1016\/j.automatica.2008.11.017","article-title":"Barrier Lyapunov functions for the control of output-constrained nonlinear systems","volume":"45","author":"Tee","year":"2009","journal-title":"Automatica"},{"issue":"5","key":"10.1016\/j.neunet.2026.109752_bib0022","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1016\/j.automatica.2010.02.018","article-title":"Online actor\u2013critic algorithm to solve the continuous-time infinite horizon optimal control problem","volume":"46","author":"Vamvoudakis","year":"2010","journal-title":"Automatica"},{"issue":"1","key":"10.1016\/j.neunet.2026.109752_bib0023","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1109\/TAC.2021.3049335","article-title":"Probabilistic model predictive safety certification for learning-based control","volume":"67","author":"Wabersich","year":"2022","journal-title":"IEEE Transactions on Automatic Control"},{"key":"10.1016\/j.neunet.2026.109752_bib0024","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2021.109597","article-title":"A predictive safety filter for learning-based control of constrained nonlinear dynamical systems","volume":"129","author":"Wabersich","year":"2021","journal-title":"Automatica"},{"issue":"1","key":"10.1016\/j.neunet.2026.109752_bib0025","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1109\/JAS.2023.123843","article-title":"Recent progress in reinforcement learning and adaptive dynamic programming for advanced control applications","volume":"11","author":"Wang","year":"2024","journal-title":"IEEE\/CAA Journal of Automatica Sinica"},{"key":"10.1016\/j.neunet.2026.109752_bib0026","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.neunet.2021.05.027","article-title":"Neural optimal tracking control of constrained nonaffine systems with a wastewater treatment application","volume":"143","author":"Wang","year":"2021","journal-title":"Neural Networks"},{"issue":"1","key":"10.1016\/j.neunet.2026.109752_bib0027","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1109\/TITS.2022.3213413","article-title":"Robustness analysis of platoon control for mixed types of vehicles","volume":"24","author":"Wang","year":"2023","journal-title":"IEEE Transactions on Intelligent Transportation Systems"},{"key":"10.1016\/j.neunet.2026.109752_bib0028","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2022.110531","article-title":"Secure and collision-free multi-platoon control of automated vehicles under data falsification attacks","volume":"145","author":"Xiao","year":"2022","journal-title":"Automatica"},{"key":"10.1016\/j.neunet.2026.109752_bib0029","doi-asserted-by":"crossref","DOI":"10.1016\/j.neunet.2025.107659","article-title":"Dynamic periodic event-triggered control of stochastic complex networks with time-varying delays","volume":"190","author":"Yang","year":"2025","journal-title":"Neural Networks"},{"issue":"7","key":"10.1016\/j.neunet.2026.109752_bib0030","doi-asserted-by":"crossref","first-page":"4461","DOI":"10.1109\/TSMC.2024.3382356","article-title":"Adaptive optimal control via continuous-time q-learning for stackelberg\u2013nash games of uncertain nonlinear systems","volume":"54","author":"Yu","year":"2024","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics: Systems"},{"issue":"9","key":"10.1016\/j.neunet.2026.109752_bib0031","first-page":"3808","article-title":"Event-triggered optimized control for nonlinear delayed stochastic systems","volume":"68","author":"Zhang","year":"2021","journal-title":"IEEE Transactions on Circuits and Systems I: Regular Papers"}],"container-title":["Neural Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893608026012074?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893608026012074?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,11,2]],"date-time":"2026-11-02T07:57:06Z","timestamp":1793606226000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0893608026012074"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2027,2]]},"references-count":31,"alternative-id":["S0893608026012074"],"URL":"https:\/\/doi.org\/10.1016\/j.neunet.2026.109752","relation":{},"ISSN":["0893-6080"],"issn-type":[{"value":"0893-6080","type":"print"}],"subject":[],"published":{"date-parts":[[2027,2]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Lagrangian-based safe Q-learning for nonlinear delayed stochastic systems","name":"articletitle","label":"Article Title"},{"value":"Neural Networks","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.neunet.2026.109752","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"109752"}}