{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T16:22:43Z","timestamp":1781972563646,"version":"3.54.5"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"7-8","license":[{"start":{"date-parts":[[2012,11,15]],"date-time":"2012-11-15T00:00:00Z","timestamp":1352937600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2013,12]]},"DOI":"10.1007\/s00521-012-1249-y","type":"journal-article","created":{"date-parts":[[2012,11,14]],"date-time":"2012-11-14T06:35:30Z","timestamp":1352874930000},"page":"1843-1850","source":"Crossref","is-referenced-by-count":94,"title":["Adaptive optimal control for a class of continuous-time affine nonlinear systems with unknown internal dynamics"],"prefix":"10.1007","volume":"23","author":[{"given":"Derong","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiong","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongliang","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2012,11,15]]},"reference":[{"key":"1249_CR1","unstructured":"Pontryagin LS (1959) Optimal control processes. Uspehi Mat Nauk (in Russian) 14:3\u201320"},{"key":"1249_CR2","volume-title":"Dynamic programming","author":"RE Bellman","year":"1957","unstructured":"Bellman RE (1957) Dynamic programming. Princeton University Press, New Jersey"},{"key":"1249_CR3","volume-title":"Optimal control","author":"FL Lewis","year":"1995","unstructured":"Lewis FL, Syrmos VL (1995) Optimal control. John Wiley, New York"},{"issue":"6","key":"1249_CR4","doi-asserted-by":"crossref","first-page":"750","DOI":"10.1109\/TIT.1973.1055104","volume":"19","author":"T Kailath","year":"1973","unstructured":"Kailath T (1973) Some new algorithms for recursive estimation in constant linear systems. IEEE Trans Inf Theory 19(6):750\u2013760","journal-title":"IEEE Trans Inf Theory"},{"issue":"6","key":"1249_CR5","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1109\/TAC.1979.1102178","volume":"24","author":"AJ Laub","year":"1979","unstructured":"Laub AJ (1979) A Schur method for solving algebraic Riccati equations. IEEE Trans Autom Control 24(6):913\u2013921","journal-title":"IEEE Trans Autom Control"},{"key":"1249_CR6","doi-asserted-by":"crossref","unstructured":"Moris K, Navasca C (2006) Iterative solution of algebraic Riccati equations for damped systems. In: Proceedings of 45th IEEE conference on decision and control, San Diego, CA, pp 2436\u20132440","DOI":"10.1109\/CDC.2006.377430"},{"issue":"3","key":"1249_CR7","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1109\/TSMC.1979.4310171","volume":"9","author":"GN Saridis","year":"1979","unstructured":"Saridis GN, Lee CS (1979) An approximation theory of optimal control for trainable manipulators. IEEE Trans Syst Man Cybern 9(3):152\u2013159","journal-title":"IEEE Trans Syst Man Cybern"},{"issue":"12","key":"1249_CR8","doi-asserted-by":"crossref","first-page":"2159","DOI":"10.1016\/S0005-1098(97)00128-3","volume":"33","author":"R Beard","year":"1997","unstructured":"Beard R, Saridis G, Wen J (1997) Galerkin approximations of the generalized Hamilton\u2013Jacobi\u2013Bellman equation. Automatica 33(12):2159\u20132177","journal-title":"Automatica"},{"issue":"5","key":"1249_CR9","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1016\/j.automatica.2004.11.034","volume":"41","author":"M Abu-Khalaf","year":"2005","unstructured":"Abu-Khalaf M, Lewis FL (2005) Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach. Automatica 41(5):779\u2013791","journal-title":"Automatica"},{"issue":"2","key":"1249_CR10","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1109\/TSMCC.2002.801727","volume":"32","author":"JJ Murray","year":"2002","unstructured":"Murray JJ, Cox CJ, Lendaris GG, Saeks R (2002) Adaptive dynamic programming. IEEE Transa Syst Man Cybern C Appl Rev 32(2):140\u2013153","journal-title":"IEEE Transa Syst Man Cybern C Appl Rev"},{"key":"1249_CR11","first-page":"493","volume-title":"Handbook of intelligent control: neural, fuzzy, and adaptive approaches.","author":"PJ Werbos","year":"1992","unstructured":"Werbos PJ (1992) Approximate dynamic programming for real-time control and neural modeling. In: White DA, Sofge DA (eds) Handbook of intelligent control: neural, fuzzy, and adaptive approaches. Van Nostrand Reinhold, New York, pp 493\u2013525"},{"issue":"2","key":"1249_CR12","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1109\/MCI.2009.932261","volume":"4","author":"FY Wang","year":"2009","unstructured":"Wang FY, Zhang H, Liu D (2009) Adaptive dynamic programming: an introduction. IEEE Comput Intell Mag 4(2):39\u201347","journal-title":"IEEE Comput Intell Mag"},{"issue":"3","key":"1249_CR13","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1109\/MCAS.2009.933854","volume":"9","author":"FL Lewis","year":"2009","unstructured":"Lewis FL, Vrabie D (2009) Reinforcement learning and adaptive dynamic programming for feedback control. IEEE Circuits Syst Mag 9(3):32\u201350","journal-title":"IEEE Circuits Syst Mag"},{"issue":"4","key":"1249_CR14","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1109\/TSMCB.2008.926614","volume":"38","author":"A Al-Tamimi","year":"2008","unstructured":"Al-Tamimi A, Lewis FL, Abu-Khalaf M (2008) Discrete-time nonlinear HJB solution using approximate dynamic programming: convergence proof. IEEE Trans Syst Man Cybern B Cybern 38(4):943\u2013949","journal-title":"IEEE Trans Syst Man Cybern B Cybern"},{"key":"1249_CR15","unstructured":"Liu D, Wang D, Zhao D (2011) Neural-network-based optimal control for a class of nonlinear discrete-time systems with control constraints using the iterative GDHP algorithm. In: Proceedings of international joint conference on neural networks, San Jose, CA, pp 53\u201360"},{"key":"1249_CR16","volume-title":"Dynamic programming and Markov processes","author":"RA Howard","year":"1960","unstructured":"Howard RA (1960) Dynamic programming and Markov processes. MIT Press, Cambridge"},{"issue":"3","key":"1249_CR17","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.neunet.2009.03.008","volume":"22","author":"D Vrabie","year":"2009","unstructured":"Vrabie D, Lewis FL (2009) Neural network approach to continuous-time direct adaptive optimal control for partially unknown nonlinear systems. Neural Netw 22(3):237\u2013246","journal-title":"Neural Netw"},{"issue":"5","key":"1249_CR18","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1016\/j.automatica.2010.02.018","volume":"46","author":"KG Vamvoudakis","year":"2010","unstructured":"Vamvoudakis KG, Lewis FL (2010) Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem. Automatica 46(5):878\u2013888","journal-title":"Automatica"},{"key":"1249_CR19","doi-asserted-by":"crossref","unstructured":"Lee JY, Park JB, Choi YH (2010) A novel generalized value iteration scheme for uncertain continuous-time linear systems. In: Proceedings of the 49th IEEE conference on decision and control, Atlanta, GA, pp 4637\u20134642","DOI":"10.1109\/CDC.2010.5718015"},{"key":"1249_CR20","unstructured":"Guo L, Cheng DZ, Feng DX (2005) Introduction to control theory: from basic concepts to research frontiers. Science Press (in Chinese), Beijing"},{"key":"1249_CR21","volume-title":"Principles of mathematical analysis (3rd edn)","author":"W Rudin","year":"1976","unstructured":"Rudin W (1976) Principles of mathematical analysis, 3rd edn. McGraw-Hill, New York"},{"issue":"5","key":"1249_CR22","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/0893-6080(90)90005-6","volume":"3","author":"K Hornik","year":"1990","unstructured":"Hornik K, Stinchcombe M, White H (1990) Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural Netw 3(5):551\u2013560","journal-title":"Neural Netw"},{"key":"1249_CR23","volume-title":"The method of weighted residuals and variational principles","author":"BA Finlayson","year":"1972","unstructured":"Finlayson BA (1972) The method of weighted residuals and variational principles. Academic Press, New York"},{"issue":"1","key":"1249_CR24","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1109\/TSMCB.2010.2043839","volume":"41","author":"FL Lewis","year":"2011","unstructured":"Lewis FL, Vamvoudakis KG (2011) Reinforcement learning for partially observable dynamic processes: adaptive dynamic programming using measured output data. IEEE Trans Syst Man Cybern B Cybern 41(1):14\u201325","journal-title":"IEEE Trans Syst Man Cybern B Cybern"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-012-1249-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-012-1249-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-012-1249-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T02:14:48Z","timestamp":1559096088000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-012-1249-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11,15]]},"references-count":24,"journal-issue":{"issue":"7-8","published-print":{"date-parts":[[2013,12]]}},"alternative-id":["1249"],"URL":"https:\/\/doi.org\/10.1007\/s00521-012-1249-y","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,11,15]]}}}