Adaptive dynamic programming-based stabilization of nonlinear systems with unknown actuator saturation

This paper addresses the stabilizing control problem for nonlinear systems subject to unknown actuator saturation by using adaptive dynamic programming algorithm. The control strategy is composed of an online nominal optimal control and a neural network (NN)-based feed-forward saturation compensator...

Full description

Saved in:

Bibliographic Details
Published in:	Nonlinear dynamics Vol. 93; no. 4; pp. 2089 - 2103
Main Authors:	Zhao, Bo, Jia, Lihao, Xia, Hongbing, Li, Yuanchun
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Netherlands 01.09.2018 Springer Nature B.V
Subjects:	Actuators Adaptive algorithms Adaptive control Automotive Engineering Classical Mechanics Computer simulation Control Control stability Control theory Dynamic programming Dynamical Systems Engineering Feedforward control Liapunov direct method Mechanical Engineering Neural networks Nonlinear analysis Nonlinear control Nonlinear systems Nonlinearity Optimal control Original Paper Saturation Stability analysis Vibration Unknown actuator saturation Continuous-time nonlinear systems Stabilizing control Adaptive dynamic programming Neural networks
ISSN:	0924-090X, 1573-269X
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	This paper addresses the stabilizing control problem for nonlinear systems subject to unknown actuator saturation by using adaptive dynamic programming algorithm. The control strategy is composed of an online nominal optimal control and a neural network (NN)-based feed-forward saturation compensator. For nominal systems without actuator saturation, a critic NN is established to deal with the Hamilton–Jacobi–Bellman equation. Thus, the online approximate nominal optimal control policy can be obtained without action NN. Then, the unknown actuator saturation, which is considered as saturation nonlinearity by simple transformation, is compensated by employing a NN-based feed-forward control loop. The stability of the closed-loop nonlinear system is analyzed to be ultimately uniformly bounded via Lyapunov’s direct method. Finally, the effectiveness of the presented control method is demonstrated by two simulation examples.
AbstractList	This paper addresses the stabilizing control problem for nonlinear systems subject to unknown actuator saturation by using adaptive dynamic programming algorithm. The control strategy is composed of an online nominal optimal control and a neural network (NN)-based feed-forward saturation compensator. For nominal systems without actuator saturation, a critic NN is established to deal with the Hamilton–Jacobi–Bellman equation. Thus, the online approximate nominal optimal control policy can be obtained without action NN. Then, the unknown actuator saturation, which is considered as saturation nonlinearity by simple transformation, is compensated by employing a NN-based feed-forward control loop. The stability of the closed-loop nonlinear system is analyzed to be ultimately uniformly bounded via Lyapunov’s direct method. Finally, the effectiveness of the presented control method is demonstrated by two simulation examples.
Author	Jia, Lihao Li, Yuanchun Zhao, Bo Xia, Hongbing
Author_xml	– sequence: 1 givenname: Bo orcidid: 0000-0002-7684-7342 surname: Zhao fullname: Zhao, Bo email: zhaobo@ia.ac.cn organization: The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences – sequence: 2 givenname: Lihao surname: Jia fullname: Jia, Lihao organization: Research Center for Brain-inspired Intelligence, Institute of Automation, Chinese Academy of Sciences – sequence: 3 givenname: Hongbing surname: Xia fullname: Xia, Hongbing organization: Department of Control Science and Engineering, Changchun University of Technology – sequence: 4 givenname: Yuanchun surname: Li fullname: Li, Yuanchun organization: Department of Control Science and Engineering, Changchun University of Technology
BookMark	eNp9kMtKAzEUhoMoWC8P4C7gOppbZ5JlEW9QcKPQXchkkpraydQko9SnN20FQbCrQzj_d07OdwIOQx8sABcEXxGM6-tECK4JwkQgzrBE4gCMyLhmiFZydghGWFKOsMSzY3CS0gJjzCgWI-AmrV5l_2Fhuw668wauYj-Puut8mKNGJ9vClHXjl_5LZ98H2DtYdi99sDrCtE7Zdgl--vwKh_AW-s8AtcmDzn3p6jzELXUGjpxeJnv-U0_By93t880Dmj7dP95MpsgwzjNqTMOtqzVrTGUck4y4Rlg-ttwRS2WDx63jsjxp1XIrdO2k0aQVrSOScFmxU3C5m1uueB9symrRDzGUlYrSseSsyBF7U1hUNRUVJyVV71Im9ilF65TxeXtNjtovFcFqo17t1KuiXm3Uq8188odcRd_puN7L0B2TSjbMbfz90__QN9rKmqk
CitedBy_id	crossref_primary_10_1007_s11071_022_07594_1 crossref_primary_10_1007_s11071_023_08496_6 crossref_primary_10_1080_00207721_2023_2209846 crossref_primary_10_1007_s11071_021_07049_z crossref_primary_10_1109_TCSII_2022_3211832 crossref_primary_10_1016_j_knosys_2021_107100 crossref_primary_10_1007_s11071_023_08349_2 crossref_primary_10_1016_j_neucom_2023_127037 crossref_primary_10_1177_09596518231162759 crossref_primary_10_1007_s11071_019_05301_1 crossref_primary_10_1109_TSMC_2020_3042876 crossref_primary_10_1002_rnc_6374 crossref_primary_10_1007_s11071_021_06908_z crossref_primary_10_1002_rnc_5802 crossref_primary_10_1016_j_neunet_2022_08_010 crossref_primary_10_1155_2021_9937008 crossref_primary_10_1109_TCYB_2019_2962011 crossref_primary_10_1109_TIE_2025_3528477 crossref_primary_10_1007_s11071_019_04994_8 crossref_primary_10_1109_ACCESS_2021_3109009 crossref_primary_10_1007_s00500_020_05293_w crossref_primary_10_1007_s11071_024_10574_2 crossref_primary_10_1016_j_neucom_2019_11_032 crossref_primary_10_1007_s40747_021_00364_3 crossref_primary_10_1007_s11071_022_07624_y crossref_primary_10_1016_j_ins_2024_121542 crossref_primary_10_1016_j_ifacol_2021_04_158 crossref_primary_10_1007_s11071_023_08420_y crossref_primary_10_1007_s40747_021_00538_z crossref_primary_10_1109_ACCESS_2019_2927511 crossref_primary_10_1109_TII_2019_2925632 crossref_primary_10_1007_s41315_020_00159_8
Cites_doi	10.1016/j.ins.2015.09.001 10.1109/TNNLS.2014.2346233 10.1109/TNN.2011.2172628 10.1016/j.ins.2016.07.051 10.1016/j.automatica.2016.05.008 10.1080/00207721.2017.1296982 10.1007/s11071-013-0926-4 10.1109/TCST.2013.2296900 10.1109/72.623201 10.1007/s11071-015-2324-6 10.1109/TNN.2011.2160968 10.1109/TNNLS.2013.2281663 10.1109/TCYB.2015.2417170 10.1016/j.ins.2012.07.006 10.1109/MCI.2009.932261 10.1007/s11071-014-1347-8 10.1080/00207179.2013.848292 10.1109/TNNLS.2015.2409301 10.1109/TCST.2009.2028877 10.1007/s12555-016-0711-5 10.1109/3477.809035 10.1109/TFUZZ.2015.2505088 10.1109/TNN.2008.2000204 10.1049/iet-cta.2014.0680 10.1002/acs.2541 10.1109/TSMCB.2004.840124 10.1080/00207721.2018.1481240 10.1016/j.ins.2016.12.016 10.1109/TCYB.2015.2421338 10.1109/TNNLS.2015.2472974 10.1109/TIE.2016.2583199 10.1016/j.neucom.2016.12.063 10.1049/iet-cta.2015.1105 10.1109/72.914523 10.1109/TNNLS.2013.2280013 10.1109/TNNLS.2013.2276571 10.1613/jair.301 10.1007/978-3-319-50815-3 10.1016/j.conengprac.2016.07.014 10.1109/TSMCB.2008.926614 10.1109/TIE.2016.2609399 10.1002/acs.2786 10.1109/TSMC.2016.2592682 10.1049/iet-cta.2015.1317 10.1007/s11071-016-2954-3 10.1002/oca.2313 10.1049/iet-cta.2016.1383 10.1016/j.neucom.2010.07.005 10.1109/TNN.2009.2027233 10.1109/CDC.1995.478953 10.1109/TASE.2014.2303139 10.1109/TNNLS.2015.2461452 10.1109/TNNLS.2012.2227339 10.1109/TNNLS.2016.2586303 10.1109/TAC.2014.2309282 10.1016/j.automatica.2011.01.025
ContentType	Journal Article
Copyright	Springer Science+Business Media B.V., part of Springer Nature 2018 Copyright Springer Science & Business Media 2018 Nonlinear Dynamics is a copyright of Springer, (2018). All Rights Reserved.
Copyright_xml	– notice: Springer Science+Business Media B.V., part of Springer Nature 2018 – notice: Copyright Springer Science & Business Media 2018 – notice: Nonlinear Dynamics is a copyright of Springer, (2018). All Rights Reserved.
DBID	AAYXX CITATION 8FE 8FG ABJCF AFKRA BENPR BGLVJ CCPQU DWQXO HCIFZ L6V M7S PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS
DOI	10.1007/s11071-018-4309-8
DatabaseName	CrossRef ProQuest SciTech Collection ProQuest Technology Collection ProQuest SciTech Premium Collection Technology Collection Materials Science & Engineering Database ProQuest Central UK/Ireland ProQuest Central ProQuest Technology Collection ProQuest One ProQuest Central SciTech Premium Collection ProQuest Engineering Collection Engineering Database ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection
DatabaseTitle	CrossRef Engineering Database Technology Collection ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest One Academic UKI Edition ProQuest Central Korea Materials Science & Engineering Collection ProQuest One Academic ProQuest Central (New) Engineering Collection ProQuest One Academic (New)
DatabaseTitleList	Engineering Database
Database_xml	– sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Applied Sciences Engineering
EISSN	1573-269X
EndPage	2103
ExternalDocumentID	10_1007_s11071_018_4309_8
GrantInformation_xml	– fundername: National Natural Science Foundation of China grantid: 61603387; 61773075 funderid: http://dx.doi.org/10.13039/501100001809 – fundername: Scientific and Technological Development Plan Project in Jilin Province of China grantid: 20150520112JH; 20160414033GH – fundername: National Natural Science Foundation of China grantid: 61374051; 61502494 funderid: http://dx.doi.org/10.13039/501100001809
GroupedDBID	-5B -5G -BR -EM -Y2 -~C -~X .86 .DC .VR 06D 0R~ 0VY 123 1N0 1SB 2.D 203 28- 29N 29~ 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5QI 5VS 67Z 6NX 8FE 8FG 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFFNX AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARCEE ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BBWZM BDATZ BENPR BGLVJ BGNMA BSONS CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP EBLON EBS EIOEI EJD ESBYG F5P FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ IWAJR IXC IXD IXE IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW L6V LAK LLZTM M4Y M7S MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P9T PF0 PT4 PT5 PTHSS QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SCV SDH SDM SEG SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WH7 WK8 YLTOR Z45 Z5O Z7R Z7S Z7X Z7Y Z7Z Z83 Z86 Z88 Z8M Z8N Z8R Z8S Z8T Z8W Z8Z Z92 ZMTXR _50 ~A9 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT PQGLB DWQXO PKEHL PQEST PQQKQ PQUKI PRINS
ID	FETCH-LOGICAL-c344t-bcb4ef7a3bc6cf3931fb8e45e4f1e29b05df495e426d4e8a7f9ca1d8df1914963
IEDL.DBID	M7S
ISICitedReferencesCount	34
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000441305900020&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0924-090X
IngestDate	Tue Nov 04 22:16:13 EST 2025 Tue Nov 04 22:25:55 EST 2025 Sat Nov 29 07:48:03 EST 2025 Tue Nov 18 21:53:50 EST 2025 Fri Feb 21 02:32:36 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	4
Keywords	Unknown actuator saturation Continuous-time nonlinear systems Stabilizing control Adaptive dynamic programming Neural networks
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c344t-bcb4ef7a3bc6cf3931fb8e45e4f1e29b05df495e426d4e8a7f9ca1d8df1914963
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0002-7684-7342
PQID	2259434308
PQPubID	2043746
PageCount	15
ParticipantIDs	proquest_journals_2259434308 proquest_journals_2086728641 crossref_citationtrail_10_1007_s11071_018_4309_8 crossref_primary_10_1007_s11071_018_4309_8 springer_journals_10_1007_s11071_018_4309_8
PublicationCentury	2000
PublicationDate	2018-09-01
PublicationDateYYYYMMDD	2018-09-01
PublicationDate_xml	– month: 09 year: 2018 text: 2018-09-01 day: 01
PublicationDecade	2010
PublicationPlace	Dordrecht
PublicationPlace_xml	– name: Dordrecht
PublicationSubtitle	An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems
PublicationTitle	Nonlinear dynamics
PublicationTitleAbbrev	Nonlinear Dyn
PublicationYear	2018
Publisher	Springer Netherlands Springer Nature B.V
Publisher_xml	– name: Springer Netherlands – name: Springer Nature B.V
References	ZhaoBLiYLocal joint information based active fault tolerant control for reconfigurable manipulatorNonlinear Dyn.2014773859876322920510.1007/s11071-014-1347-81314.93041 SunLHuoWJiaoZAdaptive backstepping control of spacecraft rendezvous and proximity operations with input saturation and full-state constraintIEEE Trans. Industr. Electron.201764148049210.1109/TIE.2016.2609399 LiuDWeiQWangDYangXLiHAdaptive dynamic programming with applications in optimal control2017ChamSpringer10.1007/978-3-319-50815-31390.93003 KaelblingLPLittmanMLMooreAWReinforcement learning: a surveyJ. Artif. Intell. Res.1996423728510.1613/jair.301 XuHZhaoQJagannathanSFinite-horizon near-optimal output feedback neural network control of quantized nonlinear discrete-time systems with input constraintIEEE Trans. Neural Netw. Learn. Syst.201526817761788345497210.1109/TNNLS.2015.2409301 HePJagannathanSReinforcement learning-based output feedback control of nonlinear systems with input constraintsIEEE Trans. Syst. Man Cybern. Part B (Cybernetics)200535115015410.1109/TSMCB.2004.840124 YangXLiuDMaHXuYOnline approximate solution of HJI equation for unknown constrained-input nonlinear continuous-time systemsInform Sci.201632843545410.1016/j.ins.2015.09.00106870817 SongGLiTHuKZhengBObserver-based quantized control of nonlinear systems with input saturationNonlinear Dyn.201686211571169354656710.1007/s11071-016-2954-31349.93185 WerbosPJWhiteDASofgeDAApproximate dynamic programming for real time control and neural modelingHandbook of Intelligent Control: Neural, Fuzzy, and Adaptive Approaches1992New YorkVan Nostrand Reinhold ZhangHSongRWeiQZhangTOptimal tracking control for a class of nonlinear discrete-time systems with time delays based on heuristic dynamic programmingIEEE Trans. Neural Netw.201122121851186210.1109/TNN.2011.2172628 WuHNLiMMGuoLFinite-horizon approximate optimal guaranteed cost control of uncertain nonlinear systems with application to mars entry guidanceIEEE Trans. Neural Netw. Learn. Syst.201526714561467347991310.1109/TNNLS.2014.2346233 SiJWangYTOn-line learning control by association and reinforcementIEEE Trans. Neural Netw.20011226427610.1109/72.914523 DongLZhongXSunCHeHEvent-triggered adaptive dynamic programming for continuous-time systems with control constraintsIEEE Trans. Neural Netw. Learn.201728819411952368424410.1109/TNNLS.2016.2586303 WangFHuaCZongQAttitude control of reusable launch vehicle in reentry phase with input constraint via robust adaptive backstepping controlInt. J. Aadpt. Control.2015291013081327340784310.1002/acs.25411330.93079 ZhaiDXiaYAdaptive control for teleoperation system with varying time delays and input saturation constraintsIEEE Trans. Industr. Electron.201663116921692910.1109/TIE.2016.2583199 LiuDWangDYangXAn iterative adaptive dynamic programming algorithm for optimal control of unknown discrete-time nonlinear systems with constrained inputsInform Sci.2013220331342299368810.1016/j.ins.2012.07.0061291.49018 ZhaoBLiYLiuDSelf-tuned local feedback gain based decentralized fault tolerant control for a class of large-scale nonlinear systemsNeurocomputing201723514715610.1016/j.neucom.2016.12.063 ChenMGeSRenBAdaptive tracking control of uncertain MIMO nonlinear systems with input constraintsAutomatica2011473452465287829810.1016/j.automatica.2011.01.0251219.93053 CuiXZhangHLuoYJiangHAdaptive dynamic programming for H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\infty $$\end{document} tracking design of uncertain nonlinear systems with disturbances and input constraintsInt. J. Adapt. Control.2017311115671583373760310.1002/acs.27861386.93156 GeSHangCZhangTAdaptive neural network control of nonlinear systems by state and output feedbackIEEE Trans. Syst. Man Cybern. Part B (Cybernetics)199929681882810.1109/3477.809035 LinQWeiQZhaoBOptimal control for discrete-time systems with actuator saturationOptim. Contr. Appl. Met.20173810711080373485110.1002/oca.23131386.90164 MendozaMZavala-RłoASantibnezVReyesFOutput-feedback proportional–integral-derivative-type control with simple tuning for the global regulation of robot manipulators with input constraintsIET Control Theory Appl.201591420972106341078810.1049/iet-cta.2014.0680 ModaresHLewisFLNaghibi-SistaniMBAdaptive optimal control of unknown constrained-input systems using policy iteration and neural networksIEEE Trans. Neural Netw. Learn. Syst.201324101513152510.1109/TNNLS.2013.2276571 Bertsekas, D.P., Tsitsiklis, J.N.: Neuro-dynamic programming: an overview. In: Proceedings of the 34th IEEE Conference on Decision and Control, pp. 560–564 (1995) Al-TamimiALewisFLAbu-KhalafMDiscrete-time nonlinear HJB solution using approximate dynamic programming: Convergence proofIEEE Trans. Syst. Man Cybern. Part B (Cybernetics)200838494394910.1109/TSMCB.2008.926614 WangDMuCHeHLiuDEvent-driven adaptive robust control of nonlinear systems with uncertainties through NDP strategyIEEE Trans. Syst. Man Cybern. Syst.20174771358137010.1109/TSMC.2016.2592682 YangXLiuDWangDReinforcement learning for adaptive optimal control of unknown continuous-time nonlinear systems with input constraintsInt. J. Contr.2014873553566317252710.1080/00207179.2013.8482921317.93158 SongRLewisFLWeiQZhangHOff-policy actor-critic structure for optimal control of unknown systems with disturbancesIEEE Trans. Cybern.20164651041105010.1109/TCYB.2015.2421338 LiuDWangDLiHDecentralized stabilization for a class of continuous-time nonlinear interconnected systems using online learning optimal control approachIEEE Trans. Neural Netw. Learn. Syst.201425241842810.1109/TNNLS.2013.2280013 ProkhorovDVWunschDCAdaptive critic designsIEEE Trans. Neural Netw.199785997100710.1109/72.623201 XieCYangGApproximate guaranteed cost fault-tolerant control of unknown nonlinear systems with time-varying actuator faultsNonlinear Dyn.2016831–2269282343586710.1007/s11071-015-2324-61349.93189 ZhaoBLiuDLiYObserver based adaptive dynamic programming for fault tolerant control of a class of nonlinear systemsInform Sci.2017384213310.1016/j.ins.2016.12.016 LiDJTangLLiuYJAdaptive intelligence learning for nonlinear chaotic systemsNonlinear Dyn.201373421032109309477910.1007/s11071-013-0926-41281.34071 LiuDWeiQPolicy iteration adaptive dynamic programming algorithm for discrete-time nonlinear systemsIEEE Trans. Neural Netw. Learn. Syst.201425362163410.1109/TNNLS.2013.2281663 ZhaoBLiYModel-free adaptive dynamic programming based near-optimal decentralized tracking Control of reconfigurable manipulatorsInt. J. Control Autom. Syst.201816247849010.1007/s12555-016-0711-5 SunJLiuCFinite-horizon differential games for missile–target interception system using adaptive dynamic programming with input constraintsInt. J. Syst. Sci.2018492120376531210.1080/00207721.2018.14812401390.49049 YangXLiuDLuoBLiCData-based robust adaptive control for a class of unknown nonlinear constrained-input systems via integral reinforcement learningInform Sci.201636973174710.1016/j.ins.2016.07.051 ZhangHQinCLuoYNeural-network-based constrained optimal control scheme for discrete-time switched nonlinear system using dual heuristic programmingIEEE Trans. Autom. Sci. Eng.201411383984910.1109/TASE.2014.2303139 MehraeenSJagannathanSDecentralized optimal control of a class of interconnected nonlinear discrete-time systems by using online Hamilton–Jacobi–Bellman formulationIEEE Trans. Neural Netw.201122111757176910.1109/TNN.2011.2160968 ZhaoFGeSTuFQinYDongMAdaptive neural network control for active suspension system with actuator saturationIET Control Theory Appl.2016101416961705358527810.1049/iet-cta.2015.1317 WangDHeHZhaoBLiuDAdaptive near-optimal controllers for nonlinear decentralised feedback stabilisation problemsIET Control Theory Appl.2017116799806369976010.1049/iet-cta.2016.1383 KieferTGraichenKKugiATrajectory tracking of a 3-DOF laboratory helicopter under input and state constraintsIEEE Trans. Control Syst. Technol.201018494495210.1109/TCST.2009.2028877 GaoWJiangYJiangZPChaiTOutput-feedback adaptive optimal control of interconnected systems based on robust adaptive dynamic programmingAutomatica2016723745354291210.1016/j.automatica.2016.05.0081344.93060 ZhangHLuoYLiuDNeural-network-based near-optimal control for a class of discrete-time affine nonlinear systems with control constraintsIEEE Trans. Neural Netw.20092091490150310.1109/TNN.2009.2027233 FanQYangGAdaptive actor-critic design-based integral sliding-mode control for partially unknown nonlinear systems with input disturbancesIEEE Trans. Neural Netw. Learn. Syst.2016271165177346563110.1109/TNNLS.2015.2472974 TerraMHCerriJPIshiharaJYOptimal robust linear quadratic regulator for systems subject to uncertaintiesIEEE Trans. Automat. Control201459925862591325456010.1109/TAC.2014.23092821360.49025 FuYFuJChaiTRobust adaptive dynamic programming of two-player zero-sum games for continuous-time linear systemsIEEE Trans. Neural Netw. Learn. Syst.2015261233143319345327910.1109/TNNLS.2015.2461452 HeydariABalakrishnanSNFinite-horizon control-constrained nonlinear optimal control using single network adaptive criticsIEEE Trans. Neural Netw. Learn. Syst.201324114515710.1109/TNNLS.2012.2227339 LiuDYangXWangDWeiQReinforcement-learning-based robust controller design for continuous-time uncertain nonlinear systems subject to input constraintsIEEE Trans. Cybern.20154571372138510.1109/TCYB.2015.2417170 ChenXJiaYMatsunoFTracking control for differential-drive mobile robots with diamond-shaped input constraintsIEEE Trans. Control Syst. Technol.20142251999200610.1109/TCST.2013.2296900 BellmanREDynamic Programming1957New JerseyPrinceton University Press0077.13605 LiuYTongSLiDGaoYFuzzy adaptive control with state observer for a class of nonlinear discrete-time systems with input constraintIEEE Trans. Fuzzy Syst.20162451147115810.1109/TFUZZ.2015.2505088 ZhaoBLiuDLiYOnline fault compensation control based on policy itera X Yang (4309_CR50) 2016; 369 S Ge (4309_CR4) 1999; 29 B Zhao (4309_CR21) 2018; 16 D Zhai (4309_CR32) 2016; 63 A Heydari (4309_CR40) 2013; 24 Y Fu (4309_CR25) 2015; 26 F Wang (4309_CR28) 2015; 29 DV Prokhorov (4309_CR9) 1997; 8 S Mehraeen (4309_CR16) 2011; 22 Y Liu (4309_CR35) 2016; 24 DJ Li (4309_CR12) 2013; 73 R Song (4309_CR53) 2016; 46 LP Kaelbling (4309_CR13) 1996; 4 H Zhang (4309_CR46) 2009; 20 L Dong (4309_CR42) 2017; 28 X Yang (4309_CR49) 2016; 328 X Chen (4309_CR30) 2014; 22 Q Lin (4309_CR17) 2017; 38 D Liu (4309_CR58) 2014; 25 H Modares (4309_CR43) 2013; 24 PJ Werbos (4309_CR2) 1992 M Chen (4309_CR36) 2011; 47 J Si (4309_CR11) 2001; 12 W Gao (4309_CR18) 2016; 72 RE Bellman (4309_CR1) 1957 B Zhao (4309_CR20) 2017; 48 X Cui (4309_CR56) 2017; 31 D Wang (4309_CR26) 2017; 47 HN Wu (4309_CR54) 2015; 26 A Al-Tamimi (4309_CR8) 2008; 38 T Kiefer (4309_CR31) 2010; 18 J Sun (4309_CR34) 2018; 49 L Sun (4309_CR27) 2017; 64 D Liu (4309_CR47) 2015; 45 B Zhao (4309_CR5) 2014; 77 R Song (4309_CR45) 2010; 73 M Mendoza (4309_CR29) 2015; 9 D Liu (4309_CR3) 2017 H Xu (4309_CR44) 2015; 26 A Pomprapa (4309_CR51) 2017; 59 F Zhao (4309_CR33) 2016; 10 H Zhang (4309_CR41) 2014; 11 D Liu (4309_CR14) 2014; 25 G Song (4309_CR37) 2016; 86 X Yang (4309_CR52) 2014; 87 C Xie (4309_CR23) 2016; 83 B Zhao (4309_CR24) 2016; 10 D Wang (4309_CR15) 2017; 11 M Abu-Khalaf (4309_CR39) 2008; 19 D Liu (4309_CR48) 2013; 220 FY Wang (4309_CR7) 2009; 4 B Zhao (4309_CR6) 2017; 235 4309_CR10 B Zhao (4309_CR57) 2017; 384 Q Fan (4309_CR19) 2016; 27 H Zhang (4309_CR22) 2011; 22 MH Terra (4309_CR55) 2014; 59 P He (4309_CR38) 2005; 35
References_xml	– reference: YangXLiuDMaHXuYOnline approximate solution of HJI equation for unknown constrained-input nonlinear continuous-time systemsInform Sci.201632843545410.1016/j.ins.2015.09.00106870817 – reference: ZhangHLuoYLiuDNeural-network-based near-optimal control for a class of discrete-time affine nonlinear systems with control constraintsIEEE Trans. Neural Netw.20092091490150310.1109/TNN.2009.2027233 – reference: GeSHangCZhangTAdaptive neural network control of nonlinear systems by state and output feedbackIEEE Trans. Syst. Man Cybern. Part B (Cybernetics)199929681882810.1109/3477.809035 – reference: KaelblingLPLittmanMLMooreAWReinforcement learning: a surveyJ. Artif. Intell. Res.1996423728510.1613/jair.301 – reference: HePJagannathanSReinforcement learning-based output feedback control of nonlinear systems with input constraintsIEEE Trans. Syst. Man Cybern. Part B (Cybernetics)200535115015410.1109/TSMCB.2004.840124 – reference: SiJWangYTOn-line learning control by association and reinforcementIEEE Trans. Neural Netw.20011226427610.1109/72.914523 – reference: ZhaoBLiuDLiYObserver based adaptive dynamic programming for fault tolerant control of a class of nonlinear systemsInform Sci.2017384213310.1016/j.ins.2016.12.016 – reference: PomprapaALeonhardtSMisgeldBJEOptimal learning control of oxygen saturation using a policy iteration algorithm and a proof-of-concept in an interconnecting three-tank systemControl Eng. Pract.20175919420310.1016/j.conengprac.2016.07.014 – reference: Abu-KhalafMLewisFLHuangJNeurodynamic programming and zero-sum games for constrained control systemsIEEE Trans. Neural Netw.20081971243125210.1109/TNN.2008.2000204 – reference: SunJLiuCFinite-horizon differential games for missile–target interception system using adaptive dynamic programming with input constraintsInt. J. Syst. Sci.2018492120376531210.1080/00207721.2018.14812401390.49049 – reference: TerraMHCerriJPIshiharaJYOptimal robust linear quadratic regulator for systems subject to uncertaintiesIEEE Trans. Automat. Control201459925862591325456010.1109/TAC.2014.23092821360.49025 – reference: ChenXJiaYMatsunoFTracking control for differential-drive mobile robots with diamond-shaped input constraintsIEEE Trans. Control Syst. Technol.20142251999200610.1109/TCST.2013.2296900 – reference: ZhangHSongRWeiQZhangTOptimal tracking control for a class of nonlinear discrete-time systems with time delays based on heuristic dynamic programmingIEEE Trans. Neural Netw.201122121851186210.1109/TNN.2011.2172628 – reference: SunLHuoWJiaoZAdaptive backstepping control of spacecraft rendezvous and proximity operations with input saturation and full-state constraintIEEE Trans. Industr. Electron.201764148049210.1109/TIE.2016.2609399 – reference: SongRZhangHLuoYWeiQOptimal control laws for time-delay systems with saturating actuators based on heuristic dynamic programmingNeurocomputing201073163020302710.1016/j.neucom.2010.07.005 – reference: ChenMGeSRenBAdaptive tracking control of uncertain MIMO nonlinear systems with input constraintsAutomatica2011473452465287829810.1016/j.automatica.2011.01.0251219.93053 – reference: ZhangHQinCLuoYNeural-network-based constrained optimal control scheme for discrete-time switched nonlinear system using dual heuristic programmingIEEE Trans. Autom. Sci. Eng.201411383984910.1109/TASE.2014.2303139 – reference: CuiXZhangHLuoYJiangHAdaptive dynamic programming for H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\infty $$\end{document} tracking design of uncertain nonlinear systems with disturbances and input constraintsInt. J. Adapt. Control.2017311115671583373760310.1002/acs.27861386.93156 – reference: LiuDWangDLiHDecentralized stabilization for a class of continuous-time nonlinear interconnected systems using online learning optimal control approachIEEE Trans. Neural Netw. Learn. Syst.201425241842810.1109/TNNLS.2013.2280013 – reference: HeydariABalakrishnanSNFinite-horizon control-constrained nonlinear optimal control using single network adaptive criticsIEEE Trans. Neural Netw. Learn. Syst.201324114515710.1109/TNNLS.2012.2227339 – reference: Bertsekas, D.P., Tsitsiklis, J.N.: Neuro-dynamic programming: an overview. In: Proceedings of the 34th IEEE Conference on Decision and Control, pp. 560–564 (1995) – reference: BellmanREDynamic Programming1957New JerseyPrinceton University Press0077.13605 – reference: ProkhorovDVWunschDCAdaptive critic designsIEEE Trans. Neural Netw.199785997100710.1109/72.623201 – reference: WangFYZhangHLiuDAdaptive dynamic programming: an introductionIEEE Comput. Intell. Mag.200942394710.1109/MCI.2009.932261 – reference: WerbosPJWhiteDASofgeDAApproximate dynamic programming for real time control and neural modelingHandbook of Intelligent Control: Neural, Fuzzy, and Adaptive Approaches1992New YorkVan Nostrand Reinhold – reference: WangFHuaCZongQAttitude control of reusable launch vehicle in reentry phase with input constraint via robust adaptive backstepping controlInt. J. Aadpt. Control.2015291013081327340784310.1002/acs.25411330.93079 – reference: ZhaoBLiYLocal joint information based active fault tolerant control for reconfigurable manipulatorNonlinear Dyn.2014773859876322920510.1007/s11071-014-1347-81314.93041 – reference: LiuDWangDYangXAn iterative adaptive dynamic programming algorithm for optimal control of unknown discrete-time nonlinear systems with constrained inputsInform Sci.2013220331342299368810.1016/j.ins.2012.07.0061291.49018 – reference: ZhaoBLiuDYangXLiYObserver-critic structure-based adaptive dynamic programming for decentralised tracking control of unknown large-scale nonlinear systemsInt. J. Syst. Sci.201748919781989365262610.1080/00207721.2017.12969821371.93032 – reference: ZhaiDXiaYAdaptive control for teleoperation system with varying time delays and input saturation constraintsIEEE Trans. Industr. Electron.201663116921692910.1109/TIE.2016.2583199 – reference: WuHNLiMMGuoLFinite-horizon approximate optimal guaranteed cost control of uncertain nonlinear systems with application to mars entry guidanceIEEE Trans. Neural Netw. Learn. Syst.201526714561467347991310.1109/TNNLS.2014.2346233 – reference: WangDMuCHeHLiuDEvent-driven adaptive robust control of nonlinear systems with uncertainties through NDP strategyIEEE Trans. Syst. Man Cybern. Syst.20174771358137010.1109/TSMC.2016.2592682 – reference: LiuDYangXWangDWeiQReinforcement-learning-based robust controller design for continuous-time uncertain nonlinear systems subject to input constraintsIEEE Trans. Cybern.20154571372138510.1109/TCYB.2015.2417170 – reference: LiDJTangLLiuYJAdaptive intelligence learning for nonlinear chaotic systemsNonlinear Dyn.201373421032109309477910.1007/s11071-013-0926-41281.34071 – reference: MendozaMZavala-RłoASantibnezVReyesFOutput-feedback proportional–integral-derivative-type control with simple tuning for the global regulation of robot manipulators with input constraintsIET Control Theory Appl.201591420972106341078810.1049/iet-cta.2014.0680 – reference: XuHZhaoQJagannathanSFinite-horizon near-optimal output feedback neural network control of quantized nonlinear discrete-time systems with input constraintIEEE Trans. Neural Netw. Learn. Syst.201526817761788345497210.1109/TNNLS.2015.2409301 – reference: YangXLiuDLuoBLiCData-based robust adaptive control for a class of unknown nonlinear constrained-input systems via integral reinforcement learningInform Sci.201636973174710.1016/j.ins.2016.07.051 – reference: LinQWeiQZhaoBOptimal control for discrete-time systems with actuator saturationOptim. Contr. Appl. Met.20173810711080373485110.1002/oca.23131386.90164 – reference: GaoWJiangYJiangZPChaiTOutput-feedback adaptive optimal control of interconnected systems based on robust adaptive dynamic programmingAutomatica2016723745354291210.1016/j.automatica.2016.05.0081344.93060 – reference: Al-TamimiALewisFLAbu-KhalafMDiscrete-time nonlinear HJB solution using approximate dynamic programming: Convergence proofIEEE Trans. Syst. Man Cybern. Part B (Cybernetics)200838494394910.1109/TSMCB.2008.926614 – reference: YangXLiuDWangDReinforcement learning for adaptive optimal control of unknown continuous-time nonlinear systems with input constraintsInt. J. Contr.2014873553566317252710.1080/00207179.2013.8482921317.93158 – reference: LiuDWeiQPolicy iteration adaptive dynamic programming algorithm for discrete-time nonlinear systemsIEEE Trans. Neural Netw. Learn. Syst.201425362163410.1109/TNNLS.2013.2281663 – reference: DongLZhongXSunCHeHEvent-triggered adaptive dynamic programming for continuous-time systems with control constraintsIEEE Trans. Neural Netw. Learn.201728819411952368424410.1109/TNNLS.2016.2586303 – reference: ZhaoBLiYModel-free adaptive dynamic programming based near-optimal decentralized tracking Control of reconfigurable manipulatorsInt. J. Control Autom. Syst.201816247849010.1007/s12555-016-0711-5 – reference: KieferTGraichenKKugiATrajectory tracking of a 3-DOF laboratory helicopter under input and state constraintsIEEE Trans. Control Syst. Technol.201018494495210.1109/TCST.2009.2028877 – reference: ZhaoBLiuDLiYOnline fault compensation control based on policy iteration algorithm for a class of affine non-linear systems with actuator failuresIET Control Theory Appl.2016101518161823358731610.1049/iet-cta.2015.1105 – reference: FanQYangGAdaptive actor-critic design-based integral sliding-mode control for partially unknown nonlinear systems with input disturbancesIEEE Trans. Neural Netw. Learn. Syst.2016271165177346563110.1109/TNNLS.2015.2472974 – reference: FuYFuJChaiTRobust adaptive dynamic programming of two-player zero-sum games for continuous-time linear systemsIEEE Trans. Neural Netw. Learn. Syst.2015261233143319345327910.1109/TNNLS.2015.2461452 – reference: SongGLiTHuKZhengBObserver-based quantized control of nonlinear systems with input saturationNonlinear Dyn.201686211571169354656710.1007/s11071-016-2954-31349.93185 – reference: LiuDWeiQWangDYangXLiHAdaptive dynamic programming with applications in optimal control2017ChamSpringer10.1007/978-3-319-50815-31390.93003 – reference: ZhaoFGeSTuFQinYDongMAdaptive neural network control for active suspension system with actuator saturationIET Control Theory Appl.2016101416961705358527810.1049/iet-cta.2015.1317 – reference: WangDHeHZhaoBLiuDAdaptive near-optimal controllers for nonlinear decentralised feedback stabilisation problemsIET Control Theory Appl.2017116799806369976010.1049/iet-cta.2016.1383 – reference: ModaresHLewisFLNaghibi-SistaniMBAdaptive optimal control of unknown constrained-input systems using policy iteration and neural networksIEEE Trans. Neural Netw. Learn. Syst.201324101513152510.1109/TNNLS.2013.2276571 – reference: ZhaoBLiYLiuDSelf-tuned local feedback gain based decentralized fault tolerant control for a class of large-scale nonlinear systemsNeurocomputing201723514715610.1016/j.neucom.2016.12.063 – reference: LiuYTongSLiDGaoYFuzzy adaptive control with state observer for a class of nonlinear discrete-time systems with input constraintIEEE Trans. Fuzzy Syst.20162451147115810.1109/TFUZZ.2015.2505088 – reference: XieCYangGApproximate guaranteed cost fault-tolerant control of unknown nonlinear systems with time-varying actuator faultsNonlinear Dyn.2016831–2269282343586710.1007/s11071-015-2324-61349.93189 – reference: MehraeenSJagannathanSDecentralized optimal control of a class of interconnected nonlinear discrete-time systems by using online Hamilton–Jacobi–Bellman formulationIEEE Trans. Neural Netw.201122111757176910.1109/TNN.2011.2160968 – reference: SongRLewisFLWeiQZhangHOff-policy actor-critic structure for optimal control of unknown systems with disturbancesIEEE Trans. Cybern.20164651041105010.1109/TCYB.2015.2421338 – volume: 328 start-page: 435 year: 2016 ident: 4309_CR49 publication-title: Inform Sci. doi: 10.1016/j.ins.2015.09.001 – volume: 26 start-page: 1456 issue: 7 year: 2015 ident: 4309_CR54 publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2014.2346233 – volume: 22 start-page: 1851 issue: 12 year: 2011 ident: 4309_CR22 publication-title: IEEE Trans. Neural Netw. doi: 10.1109/TNN.2011.2172628 – volume: 369 start-page: 731 year: 2016 ident: 4309_CR50 publication-title: Inform Sci. doi: 10.1016/j.ins.2016.07.051 – volume: 72 start-page: 37 year: 2016 ident: 4309_CR18 publication-title: Automatica doi: 10.1016/j.automatica.2016.05.008 – volume: 48 start-page: 1978 issue: 9 year: 2017 ident: 4309_CR20 publication-title: Int. J. Syst. Sci. doi: 10.1080/00207721.2017.1296982 – volume: 73 start-page: 2103 issue: 4 year: 2013 ident: 4309_CR12 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-013-0926-4 – volume: 22 start-page: 1999 issue: 5 year: 2014 ident: 4309_CR30 publication-title: IEEE Trans. Control Syst. Technol. doi: 10.1109/TCST.2013.2296900 – volume: 8 start-page: 997 issue: 5 year: 1997 ident: 4309_CR9 publication-title: IEEE Trans. Neural Netw. doi: 10.1109/72.623201 – volume: 83 start-page: 269 issue: 1–2 year: 2016 ident: 4309_CR23 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-015-2324-6 – volume: 22 start-page: 1757 issue: 11 year: 2011 ident: 4309_CR16 publication-title: IEEE Trans. Neural Netw. doi: 10.1109/TNN.2011.2160968 – volume: 25 start-page: 621 issue: 3 year: 2014 ident: 4309_CR58 publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2013.2281663 – volume: 45 start-page: 1372 issue: 7 year: 2015 ident: 4309_CR47 publication-title: IEEE Trans. Cybern. doi: 10.1109/TCYB.2015.2417170 – volume: 220 start-page: 331 year: 2013 ident: 4309_CR48 publication-title: Inform Sci. doi: 10.1016/j.ins.2012.07.006 – volume: 4 start-page: 39 issue: 2 year: 2009 ident: 4309_CR7 publication-title: IEEE Comput. Intell. Mag. doi: 10.1109/MCI.2009.932261 – volume: 77 start-page: 859 issue: 3 year: 2014 ident: 4309_CR5 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-014-1347-8 – volume: 87 start-page: 553 issue: 3 year: 2014 ident: 4309_CR52 publication-title: Int. J. Contr. doi: 10.1080/00207179.2013.848292 – volume: 26 start-page: 1776 issue: 8 year: 2015 ident: 4309_CR44 publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2015.2409301 – volume: 18 start-page: 944 issue: 4 year: 2010 ident: 4309_CR31 publication-title: IEEE Trans. Control Syst. Technol. doi: 10.1109/TCST.2009.2028877 – volume: 16 start-page: 478 issue: 2 year: 2018 ident: 4309_CR21 publication-title: Int. J. Control Autom. Syst. doi: 10.1007/s12555-016-0711-5 – volume-title: Dynamic Programming year: 1957 ident: 4309_CR1 – volume: 29 start-page: 818 issue: 6 year: 1999 ident: 4309_CR4 publication-title: IEEE Trans. Syst. Man Cybern. Part B (Cybernetics) doi: 10.1109/3477.809035 – volume: 24 start-page: 1147 issue: 5 year: 2016 ident: 4309_CR35 publication-title: IEEE Trans. Fuzzy Syst. doi: 10.1109/TFUZZ.2015.2505088 – volume: 19 start-page: 1243 issue: 7 year: 2008 ident: 4309_CR39 publication-title: IEEE Trans. Neural Netw. doi: 10.1109/TNN.2008.2000204 – volume: 9 start-page: 2097 issue: 14 year: 2015 ident: 4309_CR29 publication-title: IET Control Theory Appl. doi: 10.1049/iet-cta.2014.0680 – volume: 29 start-page: 1308 issue: 10 year: 2015 ident: 4309_CR28 publication-title: Int. J. Aadpt. Control. doi: 10.1002/acs.2541 – volume: 35 start-page: 150 issue: 1 year: 2005 ident: 4309_CR38 publication-title: IEEE Trans. Syst. Man Cybern. Part B (Cybernetics) doi: 10.1109/TSMCB.2004.840124 – volume: 49 start-page: 1 issue: 2 year: 2018 ident: 4309_CR34 publication-title: Int. J. Syst. Sci. doi: 10.1080/00207721.2018.1481240 – volume: 384 start-page: 21 year: 2017 ident: 4309_CR57 publication-title: Inform Sci. doi: 10.1016/j.ins.2016.12.016 – volume-title: Handbook of Intelligent Control: Neural, Fuzzy, and Adaptive Approaches year: 1992 ident: 4309_CR2 – volume: 46 start-page: 1041 issue: 5 year: 2016 ident: 4309_CR53 publication-title: IEEE Trans. Cybern. doi: 10.1109/TCYB.2015.2421338 – volume: 27 start-page: 165 issue: 1 year: 2016 ident: 4309_CR19 publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2015.2472974 – volume: 63 start-page: 6921 issue: 11 year: 2016 ident: 4309_CR32 publication-title: IEEE Trans. Industr. Electron. doi: 10.1109/TIE.2016.2583199 – volume: 235 start-page: 147 year: 2017 ident: 4309_CR6 publication-title: Neurocomputing doi: 10.1016/j.neucom.2016.12.063 – volume: 10 start-page: 1816 issue: 15 year: 2016 ident: 4309_CR24 publication-title: IET Control Theory Appl. doi: 10.1049/iet-cta.2015.1105 – volume: 12 start-page: 264 year: 2001 ident: 4309_CR11 publication-title: IEEE Trans. Neural Netw. doi: 10.1109/72.914523 – volume: 25 start-page: 418 issue: 2 year: 2014 ident: 4309_CR14 publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2013.2280013 – volume: 24 start-page: 1513 issue: 10 year: 2013 ident: 4309_CR43 publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2013.2276571 – volume: 4 start-page: 237 year: 1996 ident: 4309_CR13 publication-title: J. Artif. Intell. Res. doi: 10.1613/jair.301 – volume-title: Adaptive dynamic programming with applications in optimal control year: 2017 ident: 4309_CR3 doi: 10.1007/978-3-319-50815-3 – volume: 59 start-page: 194 year: 2017 ident: 4309_CR51 publication-title: Control Eng. Pract. doi: 10.1016/j.conengprac.2016.07.014 – volume: 38 start-page: 943 issue: 4 year: 2008 ident: 4309_CR8 publication-title: IEEE Trans. Syst. Man Cybern. Part B (Cybernetics) doi: 10.1109/TSMCB.2008.926614 – volume: 64 start-page: 480 issue: 1 year: 2017 ident: 4309_CR27 publication-title: IEEE Trans. Industr. Electron. doi: 10.1109/TIE.2016.2609399 – volume: 31 start-page: 1567 issue: 11 year: 2017 ident: 4309_CR56 publication-title: Int. J. Adapt. Control. doi: 10.1002/acs.2786 – volume: 47 start-page: 1358 issue: 7 year: 2017 ident: 4309_CR26 publication-title: IEEE Trans. Syst. Man Cybern. Syst. doi: 10.1109/TSMC.2016.2592682 – volume: 10 start-page: 1696 issue: 14 year: 2016 ident: 4309_CR33 publication-title: IET Control Theory Appl. doi: 10.1049/iet-cta.2015.1317 – volume: 86 start-page: 1157 issue: 2 year: 2016 ident: 4309_CR37 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-016-2954-3 – volume: 38 start-page: 1071 year: 2017 ident: 4309_CR17 publication-title: Optim. Contr. Appl. Met. doi: 10.1002/oca.2313 – volume: 11 start-page: 799 issue: 6 year: 2017 ident: 4309_CR15 publication-title: IET Control Theory Appl. doi: 10.1049/iet-cta.2016.1383 – volume: 73 start-page: 3020 issue: 16 year: 2010 ident: 4309_CR45 publication-title: Neurocomputing doi: 10.1016/j.neucom.2010.07.005 – volume: 20 start-page: 1490 issue: 9 year: 2009 ident: 4309_CR46 publication-title: IEEE Trans. Neural Netw. doi: 10.1109/TNN.2009.2027233 – ident: 4309_CR10 doi: 10.1109/CDC.1995.478953 – volume: 11 start-page: 839 issue: 3 year: 2014 ident: 4309_CR41 publication-title: IEEE Trans. Autom. Sci. Eng. doi: 10.1109/TASE.2014.2303139 – volume: 26 start-page: 3314 issue: 12 year: 2015 ident: 4309_CR25 publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2015.2461452 – volume: 24 start-page: 145 issue: 1 year: 2013 ident: 4309_CR40 publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2012.2227339 – volume: 28 start-page: 1941 issue: 8 year: 2017 ident: 4309_CR42 publication-title: IEEE Trans. Neural Netw. Learn. doi: 10.1109/TNNLS.2016.2586303 – volume: 59 start-page: 2586 issue: 9 year: 2014 ident: 4309_CR55 publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2014.2309282 – volume: 47 start-page: 452 issue: 3 year: 2011 ident: 4309_CR36 publication-title: Automatica doi: 10.1016/j.automatica.2011.01.025
SSID	ssj0003208
Score	2.3823094
Snippet	This paper addresses the stabilizing control problem for nonlinear systems subject to unknown actuator saturation by using adaptive dynamic programming...
SourceID	proquest crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	2089
SubjectTerms	Actuators Adaptive algorithms Adaptive control Automotive Engineering Classical Mechanics Computer simulation Control Control stability Control theory Dynamic programming Dynamical Systems Engineering Feedforward control Liapunov direct method Mechanical Engineering Neural networks Nonlinear analysis Nonlinear control Nonlinear systems Nonlinearity Optimal control Original Paper Saturation Stability analysis Vibration
SummonAdditionalLinks	– databaseName: SpringerLink Contemporary Journals dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT8MwDI5gcIADgwFiMFAOnECV2iZr0-OEmDhNiJd2q_KUkGBM68bvx27TFdBAgrOTNoqd2I7tz4ScCwRJVyC8XDITcLBZA8lSGcQqA2MisSyxumw2kY5GYjzObn0dd1Fnu9chyfKmbordwFNB11cEHMMCYp1sIHYJti24u39aXr8sLtvQheBY4CPEuA5lrvrEV2XUWJjfgqKlrhm2_7XKXbLjTUs6qGRhj6zZSYe0vZlJ_SEuOmT7EwbhPnEDI6d451FTNaenPmXrFcgBKjlDwYLEHNqqYpO-OTqpADbkjFZI0AXF91y6mOAT3YRKrEoBZ54WCBtazjogj8Prh6ubwDdfCDTjfB4orbh1qWRKJ9ox4JxTwvK-5S6ycabCvnHgXFnQ8IZbIVOXaRkZYRwixsGxPiQtWIw9IlRJq5RjVlidcqlcJiTYVUqGfRVFhrkuCWsu5Nojk2ODjJe8wVTGXc1hV3Pc1Vx0ycVyyrSC5fhtcK9mbe5PaJGDlCRpLBIerSaDW4hFtyHMvqw53ZB__Nfxn0afkK0YRaXMWeuR1ny2sKdkU7_Pn4vZWSnXH9Mh9Iw priority: 102 providerName: Springer Nature
Title	Adaptive dynamic programming-based stabilization of nonlinear systems with unknown actuator saturation
URI	https://link.springer.com/article/10.1007/s11071-018-4309-8 https://www.proquest.com/docview/2086728641 https://www.proquest.com/docview/2259434308
Volume	93
WOSCitedRecordID	wos000441305900020&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1573-269X dateEnd: 20241214 omitProxy: false ssIdentifier: ssj0003208 issn: 0924-090X databaseCode: M7S dateStart: 19970101 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1573-269X dateEnd: 20241214 omitProxy: false ssIdentifier: ssj0003208 issn: 0924-090X databaseCode: BENPR dateStart: 19970101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVAVX databaseName: Springer Nature - Connect here FIRST to enable access customDbUrl: eissn: 1573-269X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0003208 issn: 0924-090X databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT9wwEB61wKEcoDyqLqXIB05FFknsTZwTogjU0wpBW-0t8lNCorvbzcLvZ8ZxdltUuPSSi-PE0oznPd8AHCsCSTfIvFILxyXarFyLSvPC1GhMlF6U3sZhE9VopMbj-joF3NpUVtnLxCio3dRSjPwU-Y6gzESmzma_OU2NouxqGqHxFtYJJSGLpXu3S0ksijiRLkMfg-IR4z6rGVvn0O8hR1pxSUkG9bdeWhmbz_KjUe1cbf_vgd_DVjI42XnHITvwxk92YTsZnyxd7XYXNv9AJtyDcO70jCQhc93IepYKuX7hMifV5xjalVRZ2_Vxsmlgkw52Q89Zhw_dMorysocJBe4mTFOvCrr4rCUw0bhrH35cXX6_-MbTSAZuhZQLbqyRPlRaGFvaIJCewSgvh16G3Be1yYYuoMvlUe876ZWuQm117pQLhCOHl_0DrOFh_EdgRntjgvDK20pqE2ql0doyOhuaPHciDCDrCdLYhFdOYzPumxXSMtGwQRo2RMNGDeDLcsusA-t47eXDnm5NurdtgwxTVoUqZf7v5SVNB3DSM8Zq-cV_Hbz-sU_wriBOjKVrh7C2mD_4z7BhHxd37fwI1r9ejq5vjiJv4_Pm9ucTpzIB6g
linkProvider	ProQuest
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1bT9RAFD7BxUR9AEWMq6DzoC-aCW1ntp0-GIJcAgE3xGCyb3WuCQl01-2i4U_5Gz2nl10xyhsPPp92Om2_OdeZ7wC8UUSSbhC8UgvHJfqsXItM88Tk6EykXqTe1s0msuFQjUb56RL87M7C0LbKTifWitqNLeXItxB3RGUmIrU9-capaxRVV7sWGg0sjv31DwzZqg9He_h_3ybJwf7Z7iFvuwpwK6SccWON9CHTwtjUBoFTCkZ5OfAyxD7JTTRwAaMGj6bLSa90FnKrY6dcICo0xCuOew-WcS4D2YPlj_vD089z3S-SugdehFENZUBGXR21PqyHkRaF7opLKmuom5Zw4d7-UZGtDd3B6v_2iR7DSutSs51mDTyBJV-uwWrrXrNWeVVr8Og37sWnEHacnpCuZ-661JfnlrVb1S5RzMm4O4aeM-0dbk6qsnFgZUMsoqesYcCuGOWx2VVJqcmSaTqNMxujlOhS67vW4cudvPsz6OFk_HNgRntjgvDK20xqE3Kl0Z80OhqYOHYi9CHqAFDYlpGdGoNcFAsuacJMgZgpCDOF6sO7-S2Tho7ktos3OpwUrWaqCgRomiUqlfHfxXMM9eF9B8SF-J_PenH7YK_hweHZp5Pi5Gh4_BIeJrQK6o16G9CbTa_8Jty332fn1fRVu6IYfL1rhP4CpF5gLg
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1bS-xADA4elYM-uOpRvDsPPnkotp3Zdvoo6qIoi-CFfStzhQPHumxXf79JL7sqKojPmWmHSWaSTJIvAAeSQNI1Cq9Q3AYCbdZA8VQFsc7QmEgcT5ypmk2k_b4cDLLrps9p2Wa7tyHJuqaBUJqK8dHQ-qNp4Rt6LeQGy0BQiED-gjlBYGjkrt_cT65iHlct6UJ0MuhBYtCGNT_6xFvFNLU23wVIK73T6_x4xcuw1Jic7LiWkRWYccUqdBrzkzWHu1yFxVfYhH_AH1s1pLuQ2bppPWtSuR6QHJDyswwtS8qtrSs52aNnRQ28oUasRoguGb3zsqeCnu4KpqhaBZ18VhKcaDVrDe56Z7cn50HTlCEwXIhxoI0WzqeKa5MYz5GjXksnuk74yMWZDrvWo9PlUPNb4aRKfWZUZKX1hCSHx30dZnExbgOYVk5rz510JhVK-0wqtLe0Crs6iiz3mxC2HMlNg1hOjTP-51OsZdrVHHc1p13N5SYcTqYMa7iOrwbvtGzOm5Nb5igxSRrLREQfk9FdpGLcEGf_bbk-JX_6r61vjd6H39envfzqon-5DQsxSU2V1rYDs-PRk9uFefM8_leO9ipxfwHISABj
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Adaptive+dynamic+programming-based+stabilization+of+nonlinear+systems+with+unknown+actuator+saturation&rft.jtitle=Nonlinear+dynamics&rft.au=Zhao%2C+Bo&rft.au=Jia%2C+Lihao&rft.au=Xia%2C+Hongbing&rft.au=Li%2C+Yuanchun&rft.date=2018-09-01&rft.pub=Springer+Nature+B.V&rft.issn=0924-090X&rft.eissn=1573-269X&rft.volume=93&rft.issue=4&rft.spage=2089&rft.epage=2103&rft_id=info:doi/10.1007%2Fs11071-018-4309-8
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0924-090X&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0924-090X&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0924-090X&client=summon