Some Stochastic Gradient Algorithms for Hammerstein Systems with Piecewise Linearity
Some stochastic gradient (SG) algorithms for Hammerstein systems with piecewise linearity are developed in this paper. Due to the complexity of the nonlinear structure, the key term separation is used to transfer the nonlinear model into a regression model, and then, some SG algorithms are proposed...
Uložené v:
| Vydané v: | Circuits, systems, and signal processing Ročník 40; číslo 4; s. 1635 - 1651 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York
Springer US
01.04.2021
Springer Nature B.V |
| Predmet: | |
| ISSN: | 0278-081X, 1531-5878 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | Some stochastic gradient (SG) algorithms for Hammerstein systems with piecewise linearity are developed in this paper. Due to the complexity of the nonlinear structure, the key term separation is used to transfer the nonlinear model into a regression model, and then, some SG algorithms are proposed for this model. Since the SG algorithm has slow convergence rate, a forgetting factor SG algorithm and an Aitken SG algorithm are provided. Compared with the forgetting factor SG algorithm, the Aitken SG algorithm has smaller variance of estimation error, which means the Aitken SG algorithm is more effective. Two simulation examples are provided to show the effectiveness of the proposed algorithms. |
|---|---|
| AbstractList | Some stochastic gradient (SG) algorithms for Hammerstein systems with piecewise linearity are developed in this paper. Due to the complexity of the nonlinear structure, the key term separation is used to transfer the nonlinear model into a regression model, and then, some SG algorithms are proposed for this model. Since the SG algorithm has slow convergence rate, a forgetting factor SG algorithm and an Aitken SG algorithm are provided. Compared with the forgetting factor SG algorithm, the Aitken SG algorithm has smaller variance of estimation error, which means the Aitken SG algorithm is more effective. Two simulation examples are provided to show the effectiveness of the proposed algorithms. |
| Author | Pu, Yan Yang, Yongqing Chen, Jing |
| Author_xml | – sequence: 1 givenname: Yan surname: Pu fullname: Pu, Yan organization: School of Science, Jiangnan University, School of Internet of Things Engineering, Jiangnan University – sequence: 2 givenname: Yongqing orcidid: 0000-0002-8172-6473 surname: Yang fullname: Yang, Yongqing email: yongqingyang@163.com organization: School of Science, Jiangnan University – sequence: 3 givenname: Jing surname: Chen fullname: Chen, Jing organization: School of Science, Jiangnan University |
| BookMark | eNp9kE1LAzEQhoNUsFb_gKcFz6uTzabJHkvxCwoK7cFbGLJTjXQ3NUmR9tcbXUHw4OmFmfeZj_eUjXrfE2MXHK44gLqOACDqEioogUtZl4cjNuZS8FJqpUdsDJXSJWj-fMJOY3wD4E3dVGO2WvqOimXy9hVjcra4C9g66lMx27z44NJrF4u1D8U9dh2FmMj1xXKfNdc_crt4cmTpw0UqFq4nzMj-jB2vcRPp_EcnbHV7s5rfl4vHu4f5bFFawZtUVjURNhqpEiDUdMqhbmyrrCWipm04agGkkKhtLcpWEtUWsVGopRUoxIRdDmO3wb_vKCbz5nehzxtNJfOHU6lqlV16cNngYwy0NtYlTM73KaDbGA7mK0IzRGhyhOY7QnPIaPUH3QbXYdj_D4kBitncv1D4veof6hMmLIiR |
| CitedBy_id | crossref_primary_10_1177_01423312221143777 crossref_primary_10_1109_ACCESS_2022_3158941 crossref_primary_10_1007_s00034_023_02407_1 crossref_primary_10_1007_s00034_022_02240_y crossref_primary_10_1007_s00034_022_02116_1 |
| Cites_doi | 10.1016/j.automatica.2016.01.036 10.1016/j.cam.2019.112575 10.1093/imamat/hxt027 10.1016/j.amc.2012.06.009 10.1016/j.automatica.2004.03.018 10.1016/j.jfranklin.2016.07.025 10.1002/rnc.4824 10.1109/TCYB.2017.2751558 10.1016/j.sigpro.2015.10.009 10.1016/j.jfranklin.2019.06.032 10.1109/TCYB.2015.2477366 10.1016/j.apm.2010.11.008 10.1002/rnc.4819 10.1007/s00034-017-0705-4 10.1016/j.apm.2015.03.050 10.1007/s12555-019-0191-5 10.1007/s12555-019-0140-3 10.1049/iet-spr.2019.0481 10.15388/NA.2018.6.6 10.1016/S0005-1098(97)00198-2 10.1049/iet-cta.2019.0112 10.1016/j.jfranklin.2019.11.003 10.1016/j.sysconle.2014.01.004 10.1109/TNNLS.2015.2448549 10.1049/iet-cta.2015.1056 10.1016/j.sysconle.2018.03.003 10.1016/j.ins.2018.01.029 10.1007/s11071-017-3910-6 10.1049/iet-cta.2016.0202 10.1016/j.automatica.2008.02.016 10.1002/acs.3053 10.1016/j.jfranklin.2020.03.027 10.1016/S0005-1098(01)00281-3 10.1007/s00034-016-0378-4 10.1109/TNNLS.2015.2425933 10.1177/1077546310376989 10.1016/j.amc.2016.03.036 10.1080/00207177208932130 10.1177/0954405411422327 10.1002/rnc.4961 10.1016/j.na.2005.04.041 10.1016/j.apm.2011.05.049 10.1016/j.dsp.2010.06.006 10.1007/s12555-017-0482-7 10.1016/j.sysconle.2006.08.001 10.1002/acs.2995 10.1007/s12555-016-0081-z 10.3934/mbe.2018069 |
| ContentType | Journal Article |
| Copyright | Springer Science+Business Media, LLC, part of Springer Nature 2020 Springer Science+Business Media, LLC, part of Springer Nature 2020. |
| Copyright_xml | – notice: Springer Science+Business Media, LLC, part of Springer Nature 2020 – notice: Springer Science+Business Media, LLC, part of Springer Nature 2020. |
| DBID | AAYXX CITATION 3V. 7SC 7SP 7XB 88I 8AL 8AO 8FD 8FE 8FG 8FK ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ JQ2 K7- L6V L7M L~C L~D M0N M2P M7S P5Z P62 PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U S0W |
| DOI | 10.1007/s00034-020-01554-z |
| DatabaseName | CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts Electronics & Communications Abstracts ProQuest Central (purchase pre-March 2016) Science Database (Alumni Edition) Computing Database (Alumni Edition) ProQuest Pharma Collection Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Technology Collection ProQuest One ProQuest Central ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Computing Database Science Database Engineering Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic 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 ProQuest Central Basic DELNET Engineering & Technology Collection |
| DatabaseTitle | CrossRef Computer Science Database ProQuest Central Student Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Pharma Collection ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies Database with Aerospace Engineering Collection Advanced Technologies & Aerospace Collection ProQuest Computing Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest One Academic Eastern Edition Electronics & Communications Abstracts ProQuest Technology Collection ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition ProQuest DELNET Engineering and Technology Collection Materials Science & Engineering Collection ProQuest One Academic ProQuest Central (Alumni) ProQuest One Academic (New) |
| DatabaseTitleList | Computer Science Database |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1531-5878 |
| EndPage | 1651 |
| ExternalDocumentID | 10_1007_s00034_020_01554_z |
| GrantInformation_xml | – fundername: National Natural Science Foundation of China grantid: 61973137 funderid: http://dx.doi.org/10.13039/501100001809 – fundername: the Fundamental Research Funds for the Central Universities grantid: JUSRP22016 – fundername: the Funds of the Science and Technology on Near-Surface Detection Laboratory grantid: TCGZ2019A001 |
| GroupedDBID | -5B -5G -BR -EM -Y2 -~C -~X .86 .VR 06D 0R~ 0VY 1N0 1SB 2.D 203 28- 29B 29~ 2J2 2JN 2JY 2KG 2LR 2P1 2VQ 2~H 30V 3V. 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 88I 8AO 8FE 8FG 8FW 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 ABHQN ABJCF ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACGOD ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV 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 AFEXP 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 ARAPS ARCEE ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN AZQEC B-. BA0 BBWZM BDATZ BENPR BGLVJ BGNMA BPHCQ BSONS CAG CCPQU COF CSCUP DDRTE DL5 DNIVK DPUIP DWQXO EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I-F IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X J-C J0Z JBSCW JCJTX JZLTJ K6V K7- KDC KOV KOW L6V LAS LLZTM M0N M2P M4Y M7S MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P2P P62 P9P PF0 PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZK S0W 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 TN5 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z7R Z7S Z7X Z7Z Z83 Z88 Z8M Z8N Z8R Z8T Z8W 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 7SC 7SP 7XB 8AL 8FD 8FK JQ2 L7M L~C L~D PKEHL PQEST PQUKI PRINS Q9U |
| ID | FETCH-LOGICAL-c319t-24eea98ae23037661049cd7cceee9d91a830e7aeeddca5d5ee4caa97a85c3a33 |
| IEDL.DBID | P5Z |
| ISICitedReferencesCount | 6 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000574116800001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0278-081X |
| IngestDate | Fri Nov 07 23:29:16 EST 2025 Tue Nov 18 22:17:25 EST 2025 Sat Nov 29 01:55:14 EST 2025 Fri Feb 21 02:48:50 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Keywords | Gradient search Parameter estimation Aitken method Forgetting factor Piecewise linearity |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c319t-24eea98ae23037661049cd7cceee9d91a830e7aeeddca5d5ee4caa97a85c3a33 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-8172-6473 |
| PQID | 2500165747 |
| PQPubID | 30136 |
| PageCount | 17 |
| ParticipantIDs | proquest_journals_2500165747 crossref_citationtrail_10_1007_s00034_020_01554_z crossref_primary_10_1007_s00034_020_01554_z springer_journals_10_1007_s00034_020_01554_z |
| PublicationCentury | 2000 |
| PublicationDate | 20210400 2021-04-00 20210401 |
| PublicationDateYYYYMMDD | 2021-04-01 |
| PublicationDate_xml | – month: 4 year: 2021 text: 20210400 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York – name: Cambridge |
| PublicationSubtitle | CSSP |
| PublicationTitle | Circuits, systems, and signal processing |
| PublicationTitleAbbrev | Circuits Syst Signal Process |
| PublicationYear | 2021 |
| Publisher | Springer US Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer Nature B.V |
| References | Chen, Wang, Ding (CR9) 2012; 36 Li, Liu (CR23) 2020; 18 Li, O’Regan, Akca (CR25) 2015; 80 Pan, Ma, Zhang (CR33) 2020; 14 Liu, Lam, Yu, Chen (CR27) 2016; 27 Chen (CR7) 2011; 17 Ding, Liu, Liu (CR11) 2011; 21 Ding, Xu, Meng (CR14) 2020; 369 Wang, Hayat, Alsaedi (CR39) 2016; 10 Hu, Sui, Lv, Li (CR19) 2018; 23 Ma, Xiong (CR30) 2016; 353 Xu (CR40) 2016; 120 Bai (CR2) 1998; 34 Xu, Ding (CR41) 2018; 37 Oktem (CR31) 2005; 63 Wang, Ji, Wan, Bu (CR38) 2019; 356 Salhi, Kamoun (CR36) 2015; 39 Zhang, Liu (CR48) 2020; 357 Bottegal, Aravkin, Hjalmarsson, Pillonetto (CR4) 2016; 67 Chen, Liu, Zhu (CR8) 2018; 115 Ding, Xu, Zhu (CR15) 2016; 10 Liu, Cao, Yu, Song (CR26) 2016; 46 Ji, Zhang, Kang, Yu (CR22) 2020; 30 Yang, Li, Xi, Duan (CR44) 2018; 15 Ding, Zhang, Xu (CR16) 2019; 33 Ma, Pan (CR29) 2019; 13 Xu, Xiong, Alsaedi, Hayat (CR43) 2018; 16 Ding, Lv, Pan, Wan, Jin (CR13) 2020; 18 Pavaloiu, Catinas (CR34) 2016; 287 Liu, Su, Chen (CR28) 2016; 27 Pan, Jiang, Wan, Ding (CR32) 2017; 15 Bumbariu (CR5) 2012; 219 Chen, Zhu, Li (CR10) 2018; 91 Ji, Jiang, Wan (CR21) 2020; 357 Gan, Chen, Chen, Chen (CR17) 2018; 48 Ahmadi, Mojallali (CR1) 2011; 35 Bai (CR3) 2002; 38 Chen, Gan, Chen (CR6) 2018; 438 Hussu (CR20) 1972; 15 Xu, Ding (CR42) 2017; 36 Li, Zheng, Lin (CR24) 2014; 66 Hagenblad, Ljung, Wills (CR18) 2008; 44 Zhang, Ding, Xu, Yang (CR47) 2019; 33 Vörös (CR37) 2007; 56 Ding, Liu, Bao (CR12) 2012; 226 Philippe, Johan (CR35) 2004; 40 Zhang, Ding (CR45) 2020; 30 Zhang, Ding, Xu (CR46) 2020; 30 X Liu (1554_CR26) 2016; 46 F Ding (1554_CR16) 2019; 33 H Ma (1554_CR29) 2019; 13 L Xu (1554_CR40) 2016; 120 M Ahmadi (1554_CR1) 2011; 35 A Hagenblad (1554_CR18) 2008; 44 EW Bai (1554_CR2) 1998; 34 J Pan (1554_CR32) 2017; 15 EW Bai (1554_CR3) 2002; 38 F Ding (1554_CR11) 2011; 21 XY Liu (1554_CR28) 2016; 27 F Ding (1554_CR14) 2020; 369 F Ding (1554_CR15) 2016; 10 J Chen (1554_CR10) 2018; 91 Y Ji (1554_CR22) 2020; 30 J Vörös (1554_CR37) 2007; 56 J Chen (1554_CR8) 2018; 115 JX Ma (1554_CR30) 2016; 353 Y Ji (1554_CR21) 2020; 357 MH Li (1554_CR23) 2020; 18 C Philippe (1554_CR35) 2004; 40 X Zhang (1554_CR46) 2020; 30 X Liu (1554_CR27) 2016; 27 L Xu (1554_CR43) 2018; 16 JS Li (1554_CR24) 2014; 66 XH Wang (1554_CR39) 2016; 10 GY Chen (1554_CR6) 2018; 438 H Salhi (1554_CR36) 2015; 39 I Pavaloiu (1554_CR34) 2016; 287 L Xu (1554_CR42) 2017; 36 X Li (1554_CR25) 2015; 80 J Chen (1554_CR9) 2012; 36 X Zhang (1554_CR45) 2020; 30 F Ding (1554_CR12) 2012; 226 X Yang (1554_CR44) 2018; 15 F Ding (1554_CR13) 2020; 18 A Hussu (1554_CR20) 1972; 15 LJ Wang (1554_CR38) 2019; 356 J Chen (1554_CR7) 2011; 17 M Gan (1554_CR17) 2018; 48 G Bottegal (1554_CR4) 2016; 67 J Pan (1554_CR33) 2020; 14 X Zhang (1554_CR47) 2019; 33 O Bumbariu (1554_CR5) 2012; 219 H Oktem (1554_CR31) 2005; 63 L Xu (1554_CR41) 2018; 37 X Zhang (1554_CR48) 2020; 357 JT Hu (1554_CR19) 2018; 23 |
| References_xml | – volume: 120 start-page: 660 year: 2016 end-page: 667 ident: CR40 article-title: The damping iterative parameter identification method for dynamical systems based on the sine signal measurement publication-title: Signal Process. – volume: 36 start-page: 238 year: 2012 end-page: 243 ident: CR9 article-title: Gradient based estimation algorithm for Hammerstein systems with saturation and dead-zone nonlinearities publication-title: Appl. Math. Modell. – volume: 15 start-page: 1189 issue: 3 year: 2017 end-page: 1197 ident: CR32 article-title: A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems publication-title: Int. J. Control Autom. Syst. – volume: 37 start-page: 3046 issue: 7 year: 2018 end-page: 3069 ident: CR41 article-title: Iterative parameter estimation for signal models based on measured data publication-title: Circuits Syst. Signal Process. – volume: 30 start-page: 1351 issue: 4 year: 2020 end-page: 1372 ident: CR45 article-title: Adaptive parameter estimation for a general dynamical system with unknown states publication-title: Int. J. Robust Nonlinear Control – volume: 357 start-page: 5019 issue: 8 year: 2020 end-page: 5032 ident: CR21 article-title: Hierarchical least squares parameter estimation algorithm for two-input Hammerstein finite impulse response systems publication-title: J. Frankl. Inst. – volume: 91 start-page: 797 issue: 2 year: 2018 end-page: 807 ident: CR10 article-title: Biased compensation recursive least squares algorithm for rational models publication-title: Nonlinear Dyn. – volume: 66 start-page: 104 year: 2014 end-page: 110 ident: CR24 article-title: Recursive identification of time-varying systems: Self-tuning and matrix RLS algorithms publication-title: Syst. Control Lett. – volume: 14 start-page: 455 issue: 7 year: 2020 end-page: 466 ident: CR33 article-title: Recursive coupled projection algorithms for multivariable output-error-like systems with coloured noises publication-title: IET Signal Process. – volume: 18 start-page: 886 issue: 4 year: 2020 end-page: 896 ident: CR13 article-title: Two-stage gradient-based iterative estimation methods for controlled autoregressive systems using the measurement data publication-title: Int. J. Control Autom. Syst. – volume: 357 start-page: 726 issue: 1 year: 2020 end-page: 747 ident: CR48 article-title: Recursive identification of bilinear time-delay systems through the redundant rule publication-title: J. Frankl. Inst. – volume: 13 start-page: 3040 issue: 18 year: 2019 end-page: 3051 ident: CR29 article-title: Partially-coupled least squares based iterative parameter estimation for multi-variable output-error-like autoregressive moving average systems publication-title: IET Control Theory Appl. – volume: 46 start-page: 2360 issue: 10 year: 2016 end-page: 2371 ident: CR26 article-title: Nonsmooth finite-time synchronization of switched coupled neural networks publication-title: IEEE Trans. Cybern. – volume: 10 start-page: 2506 issue: 18 year: 2016 end-page: 2514 ident: CR15 article-title: Performance analysis of the generalised projection identification for time-varying systems publication-title: IET Control Theory Appl. – volume: 40 start-page: 1543 issue: 9 year: 2004 end-page: 1550 ident: CR35 article-title: Hammerstein–Wiener system estimator initialization publication-title: Automatica – volume: 353 start-page: 4280 issue: 16 year: 2016 end-page: 4299 ident: CR30 article-title: Data filtering based forgetting factor stochastic gradient algorithm for Hammerstein systems with saturation and preload nonlinearities publication-title: J. Frankl. Inst. – volume: 36 start-page: 1735 issue: 4 year: 2017 end-page: 1753 ident: CR42 article-title: Recursive least squares and multi-innovation stochastic gradient parameter estimation methods for signal modeling publication-title: Circuits Syst. Signal Process. – volume: 39 start-page: 4951 issue: 16 year: 2015 end-page: 4962 ident: CR36 article-title: A recursive parametric estimation algorithm of multivariable nonlinear systems described by Hammerstein mathematical models publication-title: Appl. Math. Modell. – volume: 23 start-page: 904 issue: 6 year: 2018 end-page: 920 ident: CR19 article-title: Fixed-time control of delayed neural networks with impulsive perturbations publication-title: Nonlinear Anal.: Modell. Control – volume: 16 start-page: 1756 issue: 4 year: 2018 end-page: 1764 ident: CR43 article-title: Hierarchical parameter estimation for the frequency response based on the dynamical window data publication-title: Int. J. Control Autom. Syst. – volume: 48 start-page: 2866 issue: 10 year: 2018 end-page: 2874 ident: CR17 article-title: On some separated algorithms for separable nonlinear squares problems publication-title: IEEE Trans. Cybern. – volume: 17 start-page: 1281 issue: 9 year: 2011 end-page: 1286 ident: CR7 article-title: Modified stochastic gradient algorithms with fast convergence rates publication-title: J. Vib. Control – volume: 56 start-page: 99 issue: 2 year: 2007 end-page: 105 ident: CR37 article-title: Parameter identification of Wiener systems with multisegment piecewise-linear nonlinearities publication-title: Syst. Control Lett. – volume: 33 start-page: 1601 issue: 11 year: 2019 end-page: 1608 ident: CR16 article-title: The innovation algorithms for multivariable state-space models publication-title: Int. J. Adapt. Control Signal Process. – volume: 115 start-page: 15 year: 2018 end-page: 21 ident: CR8 article-title: Multi-step-length gradient iterative algorithm for equation-error type models publication-title: Syst. Control Lett. – volume: 38 start-page: 853 issue: 5 year: 2002 end-page: 860 ident: CR3 article-title: Identification of linear systems with hard input nonlinearities of known structure publication-title: Automatica – volume: 30 start-page: 1373 issue: 4 year: 2020 end-page: 1393 ident: CR46 article-title: Recursive parameter estimation methods and convergence analysis for a special class of nonlinear systems publication-title: Int. J. Robust Nonlinear Control – volume: 226 start-page: 43 issue: 1 year: 2012 end-page: 55 ident: CR12 article-title: Gradient based and least squares based iterative estimation algorithms for multi-input multi-output systems publication-title: Proc. Inst. Mech. Eng. Part I: J. Syst. Control Eng. – volume: 67 start-page: 114 year: 2016 end-page: 126 ident: CR4 article-title: Robust EM kernel-based methods for linear system identification publication-title: Automatica – volume: 44 start-page: 2697 issue: 11 year: 2008 end-page: 2705 ident: CR18 article-title: Maximum likelihood identification of Wiener models publication-title: Automatica – volume: 80 start-page: 85 issue: 1 year: 2015 end-page: 99 ident: CR25 article-title: Global exponential stabilization of impulsive neural networks with unbounded continuously distributed delays publication-title: IMA J. Appl. Math. – volume: 356 start-page: 10102 issue: 16 year: 2019 end-page: 10122 ident: CR38 article-title: Hierarchical recursive generalized extended least squares estimation algorithms for a class of nonlinear stochastic systems with colored noise publication-title: J. Frankl. Inst. – volume: 10 start-page: 1503 issue: 13 year: 2016 end-page: 1512 ident: CR39 article-title: Combined state and multi-innovation parameter estimation for an input nonlinear state space system using the key term separation publication-title: IET Control Theory Appl. – volume: 34 start-page: 333 issue: 3 year: 1998 end-page: 338 ident: CR2 article-title: An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems publication-title: Automatica – volume: 35 start-page: 1969 issue: 4 year: 2011 end-page: 1982 ident: CR1 article-title: Identification of multiple-input single-output Hammerstein models using Bezier curves and Bernstein polynomials publication-title: Appl. Math. Modell. – volume: 33 start-page: 875 issue: 6 year: 2019 end-page: 889 ident: CR47 article-title: Highly computationally efficient state filter based on the delta operator publication-title: Int. J. Adapt. Control Signal Process. – volume: 15 start-page: 1495 issue: 6 year: 2018 end-page: 1515 ident: CR44 article-title: Review of stability and stabilization for impulsive delayed systems publication-title: Math. Biosci. Eng. – volume: 27 start-page: 853 issue: 4 year: 2016 end-page: 862 ident: CR27 article-title: Finite-time consensus of multiagent systems with a switching protocol publication-title: IEEE Trans. Neural Netw. Learn. Syst. – volume: 21 start-page: 215 issue: 2 year: 2011 end-page: 238 ident: CR11 article-title: Identification methods for Hammerstein nonlinear systems publication-title: Digit. Signal Process – volume: 15 start-page: 79 issue: 1 year: 1972 end-page: 82 ident: CR20 article-title: The conjugate-gradient method for optimal control problems with undetermined final time publication-title: Int. J. Control – volume: 18 start-page: 1581 issue: 6 year: 2020 end-page: 1592 ident: CR23 article-title: Maximum likelihood least squares based iterative estimation for a class of bilinear systems using the data filtering technique publication-title: Int. J. Control Autom. Syst. – volume: 30 start-page: 3727 issue: 9 year: 2020 end-page: 3752 ident: CR22 article-title: Parameter estimation for block-oriented nonlinear systems using the key term separation publication-title: Int. J. Robust Nonlinear Control – volume: 27 start-page: 471 issue: 2 year: 2016 end-page: 482 ident: CR28 article-title: A switching approach to designing finite-time synchronization controllers of coupled neural networks publication-title: IEEE Trans. Neural Netw. Learn. Syst. – volume: 63 start-page: 336 issue: 3 year: 2005 end-page: 349 ident: CR31 article-title: A survey on piecewise-linear models of regulatory dynamical systems publication-title: Nonlinear Anal.: Theory, Method Appl. – volume: 287 start-page: 224 year: 2016 end-page: 231 ident: CR34 article-title: On a robust Aitken–Newton method based on the Hermite polynomial publication-title: Appl. Math. Comput. – volume: 438 start-page: 46 year: 2018 end-page: 57 ident: CR6 article-title: Generalized exponential autoregressive models for nonlinear time series: Stationarity, estimation and applications publication-title: Inf. Sci. – volume: 369 start-page: 112575 year: 2020 ident: CR14 article-title: Gradient estimation algorithms for the parameter identification of bilinear systems using the auxiliary model publication-title: J. Comput. Appl. Math. – volume: 219 start-page: 78 issue: 1 year: 2012 end-page: 82 ident: CR5 article-title: A new Aitken type method for accelerating iterative sequences publication-title: Appl. Math. Comput. – volume: 67 start-page: 114 year: 2016 ident: 1554_CR4 publication-title: Automatica doi: 10.1016/j.automatica.2016.01.036 – volume: 369 start-page: 112575 year: 2020 ident: 1554_CR14 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2019.112575 – volume: 80 start-page: 85 issue: 1 year: 2015 ident: 1554_CR25 publication-title: IMA J. Appl. Math. doi: 10.1093/imamat/hxt027 – volume: 219 start-page: 78 issue: 1 year: 2012 ident: 1554_CR5 publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2012.06.009 – volume: 40 start-page: 1543 issue: 9 year: 2004 ident: 1554_CR35 publication-title: Automatica doi: 10.1016/j.automatica.2004.03.018 – volume: 353 start-page: 4280 issue: 16 year: 2016 ident: 1554_CR30 publication-title: J. Frankl. Inst. doi: 10.1016/j.jfranklin.2016.07.025 – volume: 30 start-page: 1373 issue: 4 year: 2020 ident: 1554_CR46 publication-title: Int. J. Robust Nonlinear Control doi: 10.1002/rnc.4824 – volume: 48 start-page: 2866 issue: 10 year: 2018 ident: 1554_CR17 publication-title: IEEE Trans. Cybern. doi: 10.1109/TCYB.2017.2751558 – volume: 120 start-page: 660 year: 2016 ident: 1554_CR40 publication-title: Signal Process. doi: 10.1016/j.sigpro.2015.10.009 – volume: 356 start-page: 10102 issue: 16 year: 2019 ident: 1554_CR38 publication-title: J. Frankl. Inst. doi: 10.1016/j.jfranklin.2019.06.032 – volume: 46 start-page: 2360 issue: 10 year: 2016 ident: 1554_CR26 publication-title: IEEE Trans. Cybern. doi: 10.1109/TCYB.2015.2477366 – volume: 35 start-page: 1969 issue: 4 year: 2011 ident: 1554_CR1 publication-title: Appl. Math. Modell. doi: 10.1016/j.apm.2010.11.008 – volume: 30 start-page: 1351 issue: 4 year: 2020 ident: 1554_CR45 publication-title: Int. J. Robust Nonlinear Control doi: 10.1002/rnc.4819 – volume: 37 start-page: 3046 issue: 7 year: 2018 ident: 1554_CR41 publication-title: Circuits Syst. Signal Process. doi: 10.1007/s00034-017-0705-4 – volume: 39 start-page: 4951 issue: 16 year: 2015 ident: 1554_CR36 publication-title: Appl. Math. Modell. doi: 10.1016/j.apm.2015.03.050 – volume: 18 start-page: 1581 issue: 6 year: 2020 ident: 1554_CR23 publication-title: Int. J. Control Autom. Syst. doi: 10.1007/s12555-019-0191-5 – volume: 18 start-page: 886 issue: 4 year: 2020 ident: 1554_CR13 publication-title: Int. J. Control Autom. Syst. doi: 10.1007/s12555-019-0140-3 – volume: 14 start-page: 455 issue: 7 year: 2020 ident: 1554_CR33 publication-title: IET Signal Process. doi: 10.1049/iet-spr.2019.0481 – volume: 23 start-page: 904 issue: 6 year: 2018 ident: 1554_CR19 publication-title: Nonlinear Anal.: Modell. Control doi: 10.15388/NA.2018.6.6 – volume: 34 start-page: 333 issue: 3 year: 1998 ident: 1554_CR2 publication-title: Automatica doi: 10.1016/S0005-1098(97)00198-2 – volume: 13 start-page: 3040 issue: 18 year: 2019 ident: 1554_CR29 publication-title: IET Control Theory Appl. doi: 10.1049/iet-cta.2019.0112 – volume: 357 start-page: 726 issue: 1 year: 2020 ident: 1554_CR48 publication-title: J. Frankl. Inst. doi: 10.1016/j.jfranklin.2019.11.003 – volume: 66 start-page: 104 year: 2014 ident: 1554_CR24 publication-title: Syst. Control Lett. doi: 10.1016/j.sysconle.2014.01.004 – volume: 27 start-page: 471 issue: 2 year: 2016 ident: 1554_CR28 publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2015.2448549 – volume: 10 start-page: 1503 issue: 13 year: 2016 ident: 1554_CR39 publication-title: IET Control Theory Appl. doi: 10.1049/iet-cta.2015.1056 – volume: 115 start-page: 15 year: 2018 ident: 1554_CR8 publication-title: Syst. Control Lett. doi: 10.1016/j.sysconle.2018.03.003 – volume: 438 start-page: 46 year: 2018 ident: 1554_CR6 publication-title: Inf. Sci. doi: 10.1016/j.ins.2018.01.029 – volume: 91 start-page: 797 issue: 2 year: 2018 ident: 1554_CR10 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-017-3910-6 – volume: 10 start-page: 2506 issue: 18 year: 2016 ident: 1554_CR15 publication-title: IET Control Theory Appl. doi: 10.1049/iet-cta.2016.0202 – volume: 44 start-page: 2697 issue: 11 year: 2008 ident: 1554_CR18 publication-title: Automatica doi: 10.1016/j.automatica.2008.02.016 – volume: 33 start-page: 1601 issue: 11 year: 2019 ident: 1554_CR16 publication-title: Int. J. Adapt. Control Signal Process. doi: 10.1002/acs.3053 – volume: 357 start-page: 5019 issue: 8 year: 2020 ident: 1554_CR21 publication-title: J. Frankl. Inst. doi: 10.1016/j.jfranklin.2020.03.027 – volume: 38 start-page: 853 issue: 5 year: 2002 ident: 1554_CR3 publication-title: Automatica doi: 10.1016/S0005-1098(01)00281-3 – volume: 36 start-page: 1735 issue: 4 year: 2017 ident: 1554_CR42 publication-title: Circuits Syst. Signal Process. doi: 10.1007/s00034-016-0378-4 – volume: 27 start-page: 853 issue: 4 year: 2016 ident: 1554_CR27 publication-title: IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2015.2425933 – volume: 17 start-page: 1281 issue: 9 year: 2011 ident: 1554_CR7 publication-title: J. Vib. Control doi: 10.1177/1077546310376989 – volume: 287 start-page: 224 year: 2016 ident: 1554_CR34 publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2016.03.036 – volume: 15 start-page: 79 issue: 1 year: 1972 ident: 1554_CR20 publication-title: Int. J. Control doi: 10.1080/00207177208932130 – volume: 226 start-page: 43 issue: 1 year: 2012 ident: 1554_CR12 publication-title: Proc. Inst. Mech. Eng. Part I: J. Syst. Control Eng. doi: 10.1177/0954405411422327 – volume: 30 start-page: 3727 issue: 9 year: 2020 ident: 1554_CR22 publication-title: Int. J. Robust Nonlinear Control doi: 10.1002/rnc.4961 – volume: 63 start-page: 336 issue: 3 year: 2005 ident: 1554_CR31 publication-title: Nonlinear Anal.: Theory, Method Appl. doi: 10.1016/j.na.2005.04.041 – volume: 36 start-page: 238 year: 2012 ident: 1554_CR9 publication-title: Appl. Math. Modell. doi: 10.1016/j.apm.2011.05.049 – volume: 21 start-page: 215 issue: 2 year: 2011 ident: 1554_CR11 publication-title: Digit. Signal Process doi: 10.1016/j.dsp.2010.06.006 – volume: 16 start-page: 1756 issue: 4 year: 2018 ident: 1554_CR43 publication-title: Int. J. Control Autom. Syst. doi: 10.1007/s12555-017-0482-7 – volume: 56 start-page: 99 issue: 2 year: 2007 ident: 1554_CR37 publication-title: Syst. Control Lett. doi: 10.1016/j.sysconle.2006.08.001 – volume: 33 start-page: 875 issue: 6 year: 2019 ident: 1554_CR47 publication-title: Int. J. Adapt. Control Signal Process. doi: 10.1002/acs.2995 – volume: 15 start-page: 1189 issue: 3 year: 2017 ident: 1554_CR32 publication-title: Int. J. Control Autom. Syst. doi: 10.1007/s12555-016-0081-z – volume: 15 start-page: 1495 issue: 6 year: 2018 ident: 1554_CR44 publication-title: Math. Biosci. Eng. doi: 10.3934/mbe.2018069 |
| SSID | ssj0019492 |
| Score | 2.2695744 |
| Snippet | Some stochastic gradient (SG) algorithms for Hammerstein systems with piecewise linearity are developed in this paper. Due to the complexity of the nonlinear... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1635 |
| SubjectTerms | Algorithms Circuits and Systems Electrical Engineering Electronics and Microelectronics Engineering Instrumentation Linearity Regression models Signal,Image and Speech Processing |
| SummonAdditionalLinks | – databaseName: SpringerLink dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3fS8MwEA46fdAHf4vTKXnwTQNrmzbN4xCnT2O4IXsraXp1g22VtirsrzfJ0k5FBX1uGsLlku8ud_cdQpdCUC-USnlTlqSEAggiYpaS2I-lAwC-YIlpNsF6vXA04n1bFFZU2e5VSNLc1HWxm-FSIdrd0ThPyWIdbSi4YzqR72HwWMcOODWtkHVIjSjAG9lSme_n-AxHKxvzS1jUoE1393_r3EM71rrEnaU67KM1mB-g7Q-cg4doOMhmgAdlJsdCczTju9xkfZW4M33K8kk5nhVYWbLYvmnrbpjY8ppj_WqL-xOQ8DYpACtHVh0UZccfoWH3dnhzT2xrBSLVmSuJq3eFhwKUB6KuGGVDUS4TJhVkAk-4I0KvDUwoAE2k8BMfgEohOBOhLz3heceoMc_mcIJwkHqxkG7osCCmjuQcXAacBm03Bc8J2k3kVAKOpKUd190vplFNmGwEFimBRUZg0aKJrup_npekG7-OblX7FtkDWETKstOFWspZaqLrap9Wn3-e7fRvw8_QlquzXEwuTws1yvwFztGmfC0nRX5hFPMdd_7f9g priority: 102 providerName: Springer Nature |
| Title | Some Stochastic Gradient Algorithms for Hammerstein Systems with Piecewise Linearity |
| URI | https://link.springer.com/article/10.1007/s00034-020-01554-z https://www.proquest.com/docview/2500165747 |
| Volume | 40 |
| WOSCitedRecordID | wos000574116800001&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: PRVAVX databaseName: SpringerLink customDbUrl: eissn: 1531-5878 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0019492 issn: 0278-081X 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/eLvHCXMwpV1NbxMxEB2RpIf2ABSKGgiRD70Vi-xXvD5VBSUgoUarJEIRl5XXO0sj5avZLUj99R07TgKVyIWLL7u2Vvtsz3hm_B7AhVJhEGuavIXICx4iKq4yUfAsyrSHiJESuRWbEINBPJnIxAXcSldWud0T7UadL7WJkX8kU21u3pD3e7W640Y1ymRXnYRGDRqGJcFINyTRj10WQYZWFNkk1ziZvom7NGOvzllmFm4OT8ZrCPnD34Zp720-SZBau9N_8b9f_BKeO4-TXW-myCk8w8UrOPmDh_A1jEfLObJRtdS3yvA2sy9rWwlWsevZTxqyup2XjLxb5uLcRiGTOa5zZiK5LJmixt_TEhkdbmnxkG9_BuN-b_z5K3dyC1zTOqy4b5CSsUI6ldC2Q35VKHUuNJlRlLn0VBx0UCgyqrlWUR4hhlopKVQc6UAFwRuoL5YLPAfWLYJMaT_2RDcLPS0l-gJl2O34BQZet9MEb_urU-2oyI0ixizdkShbeFKCJ7XwpA9NuNz1WW2IOA6-3dpikrpFWaZ7QJrwYYvq_vG_R3t7eLR3cOybShdbz9OCerW-x_dwpH9V03Ldhsan3iAZtqH2TXBqb_zEtGLUtpOV2uHo-yNJeO7I |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3NT9swFH9CDGnjsMEYooyBD-MEFs2n48M0ofGpsgqJHnqzHOeFVoIWmgCC_2n_457dpAUkuHHgnMTyi39-3x8AP7UOg8QQeHOR5TxE1FynIudplBoPESMtMjdsQrTbSbcrT2fgX10LY9Mqa57oGHU2NNZHvkOi2lbekPb7--qa26lRNrpaj9AYw6KF93dkshW_jvfofDd9_2C_8-eIV1MFuCG4ldy3G5KJRlK-6XaR-hBKkwlD0gJlJj2dBE0UmmRHZnSURYih0VoKnUQm0Nb_SRz_A1EY2wyyluCToIUM3QxmG8vjJGm7VY2Oq9RzjWC4tdWskhLyh6dycKrcPovHOjF38OWd_aAF-Fzp02x3fAEWYQYHX2H-UZfFJeicDS-RnZVD09O2KzU7HLk8t5LtXpwTBWXvsmCku7PKi2_nf7Kqkzuzfmp22keDd_0CGZnuRCJZLt-g8xZULcPsYDjAFWBxHqTa-Ikn4jT0jJToC5Rh3PRzDLy42QCvPlllqkbrdt7HhZq0iHZoUIQG5dCgHhqwNfnmatxm5NW312oIqIrlFGp6_g3YrkE0ffzyaquvr7YBH486f0_UyXG79R0--Tanx2UurcFsObrBHzBnbst-MVp3t4GBemNw_QdNO0kQ |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3NT9swFH9CME3jAGMMUcaGD3ACi-arjg8TQmMFBKoq0UPFxXKcF6gELTSBiv5n--_27CYtQxo3DpyTWHb8e99fANtah0FsCLyZSDMeImquE5HxJEqMh4iRFqkbNiFarbjble05-FPVwti0yoonOkadDoz1ke-TqLaVN6T97mdlWkT7qHlwd8_tBCkbaa3GaUwgcoZPIzLf8p-nR3TXO77f_N35dcLLCQPcEPQK7tvNyVgjKeJEaaRKhNKkwpDkQJlKT8dBHYUmOZIaHaURYmi0lkLHkQm09YUS918Q1sQkUmpHl9MAhgzdPGYb1-MkdbtlvY6r2nNNYbi126zCEvLxvzJxpui-iM06kddcfsc_6zMslXo2O5wQxgrMYf8LLD7rvrgKnYvBLbKLYmCute1WzY6HLv-tYIc3V3SC4vo2Z6TTs9K7b-eCsrLDO7P-a9buocFRL0dGJj0dkSyar9B5i1OtwXx_0Md1YI0sSLTxY080ktAzUqIvUIaNup9h4DXqNfCqW1ambMBu54DcqGnraIcMRchQDhlqXIPd6Td3k_Yjr769WcFBlawoVzMs1GCvAtTs8f9X23h9tS34SJhS56ets2_wybepPi6haRPmi-EDfocP5rHo5cMfjjAYqDfG1l_R4FIr |
| 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=Some+Stochastic+Gradient+Algorithms+for+Hammerstein+Systems+with+Piecewise+Linearity&rft.jtitle=Circuits%2C+systems%2C+and+signal+processing&rft.au=Pu%2C+Yan&rft.au=Yang%2C+Yongqing&rft.au=Chen%2C+Jing&rft.date=2021-04-01&rft.pub=Springer+Nature+B.V&rft.issn=0278-081X&rft.eissn=1531-5878&rft.volume=40&rft.issue=4&rft.spage=1635&rft.epage=1651&rft_id=info:doi/10.1007%2Fs00034-020-01554-z&rft.externalDBID=HAS_PDF_LINK |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0278-081X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0278-081X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0278-081X&client=summon |