{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T10:14:52Z","timestamp":1782209692858,"version":"3.54.5"},"reference-count":68,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"4","license":[{"start":{"date-parts":[[2015,4,1]],"date-time":"2015-04-01T00:00:00Z","timestamp":1427846400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Basic Research Program of China (973 Program)","doi-asserted-by":"crossref","award":["2012CB720003"],"award-info":[{"award-number":["2012CB720003"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61121003"],"award-info":[{"award-number":["61121003"]}],"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":["51175519"],"award-info":[{"award-number":["51175519"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"General Research Fund through the Research Grants Council of Hong Kong SAR","award":["CityU 116212"],"award-info":[{"award-number":["CityU 116212"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Neural Netw. Learning Syst."],"published-print":{"date-parts":[[2015,4]]},"DOI":"10.1109\/tnnls.2014.2320744","type":"journal-article","created":{"date-parts":[[2014,5,19]],"date-time":"2014-05-19T14:04:10Z","timestamp":1400508250000},"page":"684-696","source":"Crossref","is-referenced-by-count":129,"title":["Adaptive Optimal Control of Highly Dissipative Nonlinear Spatially Distributed Processes With Neuro-Dynamic Programming"],"prefix":"10.1109","volume":"26","author":[{"family":"Biao Luo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"family":"Huai-Ning Wu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"family":"Han-Xiong Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref39","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.23919\/ACC.1989.4790360","article-title":"neural network control of unknown nonlinear systems","author":"li","year":"1989","journal-title":"1989 American Control Conference ACC"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2012.2196708"},{"key":"ref33","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1109\/TNNLS.2013.2281663","article-title":"Policy iteration adaptive dynamic programming algorithm for discrete-time nonlinear systems","volume":"25","author":"liu","year":"2014","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2010.2076370"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2009.2027233"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2008.920269"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2011.2166384"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2012.2227339"},{"key":"ref35","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1109\/TNN.2011.2147797","article-title":"Adaptive learning and control for MIMO system based on adaptive dynamic programming","volume":"22","author":"fu","year":"2011","journal-title":"IEEE Trans Neural Netw"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2011.2172628"},{"key":"ref60","author":"lewis","year":"2013","journal-title":"Optimal Control"},{"key":"ref62","author":"ge","year":"2001","journal-title":"Stable Adaptive Neural Network Control"},{"key":"ref61","volume":"1","author":"courant","year":"2004","journal-title":"Methods of Mathematical Physics"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1016\/S0009-2509(97)87571-9"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2008.926614"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1021\/ie300897m"},{"key":"ref27","volume":"17","author":"lewis","year":"2013","journal-title":"Reinforcement Learning and Approximate Dynamic Programming for Feedback Control"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2009.02.017"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2012.04.011"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2007.900227"},{"key":"ref67","first-page":"1204","article-title":"Convergent temporal-difference learning with arbitrary smooth function approximation","author":"maei","year":"2009","journal-title":"Advances in neural information processing systems"},{"key":"ref68","volume":"3","author":"khalil","year":"2002","journal-title":"Nonlinear Systems"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2007.899229"},{"key":"ref1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0185-4","author":"christofides","year":"2001","journal-title":"Nonlinear and Robust Control of PDE Systems Methods and Applications to Transport-Reaction Processes"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2010.11.001"},{"key":"ref22","author":"sutton","year":"1998","journal-title":"Reinforcement Learning An Introduction"},{"key":"ref21","doi-asserted-by":"crossref","first-page":"1538","DOI":"10.1109\/TSMCB.2012.2194781","article-title":"Approximate optimal control design for nonlinear one-dimensional parabolic PDE systems using empirical eigenfunctions and neural network","volume":"42","author":"luo","year":"2012","journal-title":"IEEE Trans Syst Man Cybern B Cybern"},{"key":"ref24","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1613\/jair.301","article-title":"Reinforcement learning: A survey","volume":"4","author":"kaelbling","year":"1996","journal-title":"J Artif Intell Res"},{"key":"ref23","author":"bertsekas","year":"1996","journal-title":"Neuro-Dynamic Programming"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/MCAS.2009.933854"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/MCI.2009.932261"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2014.2319577"},{"key":"ref51","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1109\/TNNLS.2013.2280013","article-title":"Decentralized stabilization for a class of continuous-time nonlinear interconnected systems using online learning optimal control approach","volume":"25","author":"liu","year":"2014","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1016\/S0009-2509(98)00091-8"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2014.02.017"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1021\/ie4031743"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-007-0741-2"},{"key":"ref55","first-page":"287","article-title":"Finite-dimensional control of nonlinear parabolic PDE systems with time-dependent spatial domains using empirical eigenfunctions","volume":"11","author":"armaou","year":"2001","journal-title":"Int J Appl Math Comput Sci"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1080\/002071700219614"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1016\/j.ces.2007.02.046"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1016\/j.compchemeng.2007.10.018"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(83)90167-1"},{"key":"ref11","author":"ray","year":"1981","journal-title":"Advanced Process Control"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2012.05.049"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(90)90061-J"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(00)00123-0"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1002\/aic.11770"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1021\/ie100463f"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1002\/aic.13854"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/S0009-2509(00)00037-3"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/ACC.2003.1239074"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2012.2192748"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/S0009-2509(02)00419-0"},{"key":"ref3","doi-asserted-by":"crossref","first-page":"1630","DOI":"10.1109\/TNN.2009.2028887","article-title":"Adaptive neural control design for nonlinear distributed parameter systems with persistent bounded disturbances","volume":"20","author":"wu","year":"2009","journal-title":"IEEE Trans Neural Netw"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2010.2046640"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1002\/aic.690470111"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(99)00013-4"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2012.2185046"},{"key":"ref49","author":"luo","year":"2013","journal-title":"Data-based approximate policy iteration for nonlinear continuous-time optimal control design arXiv preprint arXiv 1311 0396"},{"key":"ref9","author":"holmes","year":"1998","journal-title":"Turbulence Coherent Structures Dynamical Systems and Symmetry"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2008.08.017"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCC.2002.801727"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2010.02.018"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2009.03.008"},{"key":"ref42","doi-asserted-by":"crossref","first-page":"2159","DOI":"10.1016\/S0005-1098(97)00128-3","article-title":"Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation","volume":"33","author":"beard","year":"1997","journal-title":"Automatica"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2012.07.006"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1162\/089976600300015961"},{"key":"ref43","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1016\/j.automatica.2004.11.034","article-title":"Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach","volume":"41","author":"abu-khalaf","year":"2005","journal-title":"Automatica"}],"container-title":["IEEE Transactions on Neural Networks and Learning Systems"],"original-title":[],"link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/xplorestaging.ieee.org\/ielx7\/5962385\/7061550\/06818406.pdf?arnumber=6818406","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,12]],"date-time":"2022-01-12T11:41:41Z","timestamp":1641987701000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/ieeexplore.ieee.org\/document\/6818406\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4]]},"references-count":68,"journal-issue":{"issue":"4"},"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1109\/tnnls.2014.2320744","relation":{},"ISSN":["2162-237X","2162-2388"],"issn-type":[{"value":"2162-237X","type":"print"},{"value":"2162-2388","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4]]}}}