{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T16:19:14Z","timestamp":1783527554884,"version":"3.55.0"},"reference-count":40,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"2","license":[{"start":{"date-parts":[[2018,2,1]],"date-time":"2018-02-01T00:00:00Z","timestamp":1517443200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61603382"],"award-info":[{"award-number":["61603382"]}],"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":["61273136"],"award-info":[{"award-number":["61273136"]}],"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":["61573353"],"award-info":[{"award-number":["61573353"]}],"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":["61533017"],"award-info":[{"award-number":["61533017"]}],"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":["61503379"],"award-info":[{"award-number":["61503379"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Early Career Development Award of SKLMCCS"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Cybern."],"published-print":{"date-parts":[[2018,2]]},"DOI":"10.1109\/tcyb.2016.2643687","type":"journal-article","created":{"date-parts":[[2017,1,10]],"date-time":"2017-01-10T14:24:42Z","timestamp":1484058282000},"page":"500-509","source":"Crossref","is-referenced-by-count":70,"title":["Policy Iteration for $H_\\infty $ Optimal Control of Polynomial Nonlinear Systems via Sum of Squares Programming"],"prefix":"10.1109","volume":"48","author":[{"given":"Yuanheng","family":"Zhu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8218-9633","authenticated-orcid":false,"given":"Dongbin","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0128-3036","authenticated-orcid":false,"given":"Xiong","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qichao","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref39","doi-asserted-by":"crossref","first-page":"1884","DOI":"10.1109\/TNNLS.2012.2217349","article-title":"Neural network based online simultaneous policy update algorithm for solving the HJI equation in nonlinear ${H}_{\\infty }$ control","volume":"23","author":"wu","year":"2012","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2006.09.019"},{"key":"ref33","first-page":"191","article-title":"Approximate dynamic programming via sum of squares programming","author":"summers","year":"2013","journal-title":"Proc European Control Conf (ECC)"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1016\/S1874-1029(13)60055-5"},{"key":"ref31","doi-asserted-by":"crossref","first-page":"1892","DOI":"10.1109\/TAC.2009.2022108","article-title":"Simultaneous stabilization and robust control of polynomial nonlinear systems using SOS techniques","volume":"54","author":"xu","year":"2009","journal-title":"IEEE Trans Autom Control"},{"key":"ref30","first-page":"157","article-title":"Nonlinear control synthesis by sum of squares optimization: A Lyapunov-based approach","volume":"1","author":"prajna","year":"2004","journal-title":"Proc 5th Asian Control Conf"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2016.2574747"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2015.2414811"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1137\/16M105767X"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1109\/ACC.2014.6859382"},{"key":"ref10","author":"lewis","year":"2013","journal-title":"Reinforcement Learning and Approximate Dynamic Programming for Feedback Control"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1109\/37.588129"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/MCI.2009.932261"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/IJCNN.2012.6252630"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2009.2027233"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2013.2294968"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2016.2597763"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2013.11.055"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2006.884959"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2014.2313915"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2016.2531680"},{"key":"ref28","author":"papachristodoulou","year":"2013","journal-title":"SOSTOOLS Sum of squares optimization toolbox for Matlab"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/9.256331"},{"key":"ref27","author":"blekherman","year":"2013","journal-title":"Semidefinite Optimization and Convex Algebraic Geometry"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/9.159566"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.4590040403"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1145\/779359.779363"},{"key":"ref5","author":"burl","year":"1998","journal-title":"Linear Optimal Control $ H _ 2 $ and $H_\\infty $ Methods"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.2514\/3.21495"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.1994.411440"},{"key":"ref2","author":"bardi","year":"2008","journal-title":"Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations"},{"key":"ref9","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1080\/002071798221542","article-title":"Successive Galerkin approximation algorithms for nonlinear optimal and robust control","volume":"71","author":"beard","year":"1998","journal-title":"Int J Control"},{"key":"ref1","author":"ba?ar","year":"1995","journal-title":"$H^\\infty$ -Optimal Control and Related Minimax Design Problems"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2012.2203336"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2010.02.018"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2015.2488680"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2015.2421338"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2012.2196708"},{"key":"ref26","article-title":"Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization","author":"parrilo","year":"2000"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2016.2561300"}],"container-title":["IEEE Transactions on Cybernetics"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/6221036\/8246764\/07812594.pdf?arnumber=7812594","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,12]],"date-time":"2022-01-12T11:41:47Z","timestamp":1641987707000},"score":1,"resource":{"primary":{"URL":"http:\/\/ieeexplore.ieee.org\/document\/7812594\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2]]},"references-count":40,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.1109\/tcyb.2016.2643687","relation":{},"ISSN":["2168-2267","2168-2275"],"issn-type":[{"value":"2168-2267","type":"print"},{"value":"2168-2275","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2]]}}}