{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T03:19:01Z","timestamp":1771557541500,"version":"3.50.1"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2018,11,2]],"date-time":"2018-11-02T00:00:00Z","timestamp":1541116800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2019,9]]},"DOI":"10.1007\/s00521-018-3835-0","type":"journal-article","created":{"date-parts":[[2018,11,2]],"date-time":"2018-11-02T15:16:10Z","timestamp":1541171770000},"page":"4503-4512","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Iterative learning control for linear generalized distributed parameter system"],"prefix":"10.1007","volume":"31","author":[{"given":"Yingjun","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yinghui","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mengji","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,11,2]]},"reference":[{"key":"3835_CR1","doi-asserted-by":"publisher","first-page":"706","DOI":"10.9746\/sicetr1965.14.706","volume":"19","author":"M Uchiyama","year":"1978","unstructured":"Uchiyama M (1978) Formation of high-speed motion pattern of mechanical arm by trial. Trans Soc Instrum Control Eng 19:706\u2013712","journal-title":"Trans Soc Instrum Control Eng"},{"issue":"2P","key":"3835_CR2","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1002\/rob.4620010203","volume":"1","author":"S Arimoto","year":"1984","unstructured":"Arimoto S, Kawamura S, Miyazaki F (1984) Bettering operation of robots by learning. J Robot Syst 1(2P):123\u2013140","journal-title":"J Robot Syst"},{"key":"3835_CR3","unstructured":"Zhang J, Dai X, Tian S (2015) Iterative learning control for distributed parameter switched systems. In: Control and decision conference. IEEE, pp 105\u20131110"},{"issue":"1","key":"3835_CR4","first-page":"48","volume":"13","author":"YH Lan","year":"2016","unstructured":"Lan YH, Liu X (2016) Convergence analysis of second-order P-type iterative learning control of fractional order linear systems. Control Eng China","journal-title":"Int J Comput Sci Eng"},{"key":"3835_CR5","unstructured":"Xie S, Tian S, Fu Y (2004) A new algorithm of iterative learning control with forgetting factors. In: Control, automation, robotics and vision conference, 2004. Icarcv 2004, vol 1. IEEE, pp. 625\u2013630"},{"issue":"3","key":"3835_CR6","first-page":"264","volume":"26","author":"F Bouakrif","year":"2011","unstructured":"Bouakrif F (2011) Iterative learning control for strictly unknown nonlinear systems subject to external disturbances. Int J Control Autom Syst 9(4):642\u2013648","journal-title":"Int J Robot Autom"},{"issue":"3","key":"3835_CR7","first-page":"1","volume":"2015","author":"H Wang","year":"2015","unstructured":"Wang H, Dong J, Wang Y (2015) High-order feedback iterative learning control algorithm with forgetting factor. Math Probl Eng 2015(3):1\u20137","journal-title":"Math Probl Eng"},{"issue":"4","key":"3835_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2017\/9269187","volume":"2017","author":"T Lan","year":"2017","unstructured":"Lan T, Yan F, Lin H (2017) Iterative learning control with forgetting factor for urban road network. J Control Sci Eng 2017(4):1\u20137","journal-title":"J Control Sci Eng"},{"issue":"12","key":"3835_CR9","first-page":"1277","volume":"44","author":"ZQ Ge","year":"2014","unstructured":"Ge ZQ, Feng DX (2014) Well-posed problem of nonlinear time varying generalized distributed parameter systems. Sci China: Inf Sci 44(12):1277\u20131298","journal-title":"Sci China: Inf Sci"},{"issue":"3","key":"3835_CR10","first-page":"386","volume":"43","author":"ZQ Ge","year":"2013","unstructured":"Ge ZQ (2013) Solvability of a time-varying generalized distributed parameter system in Banach space. Sci China: Inf Sci 43(3):386\u2013406","journal-title":"Sci China: Inf Sci"},{"key":"3835_CR11","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/j.cam.2013.09.070","volume":"262","author":"J Vuong","year":"2014","unstructured":"Vuong J, Simeon B (2014) On finite element method\u2013flux corrected transport stabilization for advection\u2013diffusion problems in a partial differential\u2013algebraic framework. J Comput Appl Math 262:115\u2013126","journal-title":"J Comput Appl Math"},{"issue":"2","key":"3835_CR12","first-page":"145","volume":"115","author":"JH Yang","year":"2000","unstructured":"Yang JH, Liu YQ (2000) Sliding mode control of generalized distributed parameter perturbation system (in Chinese). Control Decis 115(2):145\u2013148","journal-title":"Control Decis"},{"key":"3835_CR13","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.sysconle.2012.10.010","volume":"62","author":"MA Demetriou","year":"2013","unstructured":"Demetriou MA (2013) Synchronization and consensus controllers for a class of parabolic distributed parameter systems. Syst Control Lett 62:70\u201376","journal-title":"Syst Control Lett"},{"issue":"2","key":"3835_CR14","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/j.jprocont.2016.08.010","volume":"48","author":"HN Wu","year":"2016","unstructured":"Wu HN, Wang HD, Guo L (2016) Finite dimensional disturbance observer based control for nonlinear parabolic PDE systems via output feedback. J Process Control 48(2):25\u201350","journal-title":"J Process Control"},{"issue":"2","key":"3835_CR15","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/j.sysconle.2014.08.003","volume":"72","author":"DQ Huang","year":"2014","unstructured":"Huang DQ, Li XF, Xu JX, Xu C, He W (2014) Iterative learning control of inhomogeneous distributed parameter systems\u2013frequency domain design and analysis. Syst Control Lett 72(2):22\u201329","journal-title":"Syst Control Lett"},{"issue":"2","key":"3835_CR16","doi-asserted-by":"publisher","first-page":"834","DOI":"10.1109\/TAC.2016.2571689","volume":"62","author":"TF Xiao","year":"2017","unstructured":"Xiao TF, Li HX (2017) Eigenspectrum-based iterative learning control for a class of distributed parameter systems. IEEE Trans Autom Control 62(2):834\u2013836","journal-title":"IEEE Trans Autom Control"},{"issue":"3","key":"3835_CR17","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1109\/JAS.2014.7004684","volume":"1","author":"XS Dai","year":"2014","unstructured":"Dai XS, Tian SP, Peng YJ, Luo WG (2014) Closed-loop P-type iterative learning control of uncertain linear distributed parameter systems. IEEE\/CAA J Sin Autom 1(3):267\u2013273","journal-title":"IEEE\/CAA J Sin Autom"},{"key":"3835_CR18","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1186\/s13662-016-0820-8","volume":"1","author":"XS Dai","year":"2016","unstructured":"Dai XS, Xu C, Tian SP, Li ZL (2016) Iterative learning control for MIMO second-order hyperbolic distributed parameter systems with uncertainties. Adv Differ Equ 1:94\u2013106","journal-title":"Adv Differ Equ"},{"issue":"6","key":"3835_CR19","first-page":"658","volume":"33","author":"FX Piao","year":"2007","unstructured":"Piao FX, Zhang QL, Wang ZF (2007) Iterative learning control for a class of generalized systems. Acta Autom Sin 33(6):658\u2013659","journal-title":"Acta Autom Sin"},{"key":"3835_CR20","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1186\/s13662-016-1047-4","volume":"1","author":"SP Tian","year":"2016","unstructured":"Tian SP, Liu Q, Dai XS, Zhang JX (2016) A PD-type iterative learning control algorithm for generalized discrete systems. Adv Differ Equ 1:321\u2013329","journal-title":"Adv Differ Equ"},{"key":"3835_CR21","first-page":"645","volume":"35","author":"T Kaczorek","year":"1987","unstructured":"Kaczorek T (1987) Generalized Rosser model and reduction to its canonical form. Bull Pol Acad Sci Tech Sci 35:645\u2013652","journal-title":"Bull Pol Acad Sci Tech Sci"},{"key":"3835_CR22","doi-asserted-by":"publisher","first-page":"1060","DOI":"10.1109\/9.14418","volume":"33","author":"T Kaczorek","year":"1988","unstructured":"Kaczorek T (1988) The generalized general model of 2-D systems and its solution. IEEE Trans Autom Control 33:1060\u20131061","journal-title":"IEEE Trans Autom Control"},{"key":"3835_CR23","unstructured":"Lewis FL (1987) Recent work in generalized systems. In: Proceedings of the International Symposium on generalized systems. Atlants, GA, pp 20\u201324"},{"key":"3835_CR24","doi-asserted-by":"crossref","unstructured":"Lewis FL, Mertzios BG (1992) On the analysis of two-dimensional discrete singular systems. Birkhauser Boston Inc","DOI":"10.1007\/BF01190984"},{"issue":"6","key":"3835_CR25","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1109\/9.24237","volume":"34","author":"T Kaczorek","year":"1989","unstructured":"Kaczorek T (1989) Decomposition of 2-d linear systems into 1-d systems in the frequency domain. IEEE Trans Autom Control 34(6):639\u2013641","journal-title":"IEEETrans Autom Control"},{"key":"3835_CR26","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1080\/00207169008803948","volume":"37","author":"L Joder","year":"1990","unstructured":"Joder L (1990) Computing accurate solutions for coupled systems of second order partial differential equations. Int J Comput Math 37:201\u2013212","journal-title":"Int J Comput Math"},{"issue":"3","key":"3835_CR27","first-page":"315","volume":"30","author":"Y Yuan","year":"2010","unstructured":"Yuan Y, Ge Z (2010) Exponential stability of the first order generalized distributed parameter systems. Syst Sci Math 30(3):315\u2013322","journal-title":"Syst Sci Math"},{"issue":"7","key":"3835_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.14257\/ijunesst.2016.9.7.01","volume":"9","author":"Y Zhang","year":"2016","unstructured":"Zhang Y, Li Y, Su J (2016) Singular distributed parameter system iterative learning control with forgetting factor with  time-delay. Int J u- e- Serv Sci Technol 9(7):1\u20138","journal-title":"Int J u- and e- Serv Sci Technol"},{"key":"3835_CR29","first-page":"9","volume":"4","author":"Q Liu","year":"1999","unstructured":"Liu Q, Yang H-J (1999) Variable structure control method of structural stability for generalized distributed parameter system. J South China Univ Technol (Nat Sci Edn) 4:9\u201312","journal-title":"J South China Univ Technol (Nat Sci Edn)"},{"key":"3835_CR30","doi-asserted-by":"crossref","unstructured":"Yang J, Wang HO (2004) Dynamic output variable structure control of generalized distributed parameter system. In: Control, automation, robotics and vision conference, 2004. ICARCV 2004, vol 2. IEEE, pp 1217\u20131221","DOI":"10.1109\/ICARCV.2004.1469018"},{"key":"3835_CR31","unstructured":"Liu F, Shi G, Luo Y (2010) An equivalent proposition for stability by feedback of the second order generalized distributed parameter system. In: International conference on advanced computer theory and engineering. IEEE, V3-71\u2013V3-74"},{"key":"3835_CR32","unstructured":"Jiang YS, Zhang QL (2016) State feedback control on generalized distributed parameter system with parabolic-elliptic type. In: Proceedings of the 35th Chinese control and decision conference. pp 261\u2013265"},{"issue":"4","key":"3835_CR33","doi-asserted-by":"publisher","first-page":"684","DOI":"10.1109\/TNNLS.2014.2320744","volume":"26","author":"B Luo","year":"2015","unstructured":"Luo B, Wu HN, Li HX (2015) Adaptive optimal control of highly dissipative nonlinear spatially distributed processes with neuro-dynamic programming. IEEE Trans. Neural Netw Learn Syst 26(4):684\u2013696","journal-title":"IEEE Trans. Neural Netw Learn Syst"},{"issue":"12","key":"3835_CR34","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11432-013-4852-3","volume":"56","author":"ZQ Ge","year":"2013","unstructured":"Ge ZQ, Feng DX (2013) Well-posed problem of nonlinear generalized distributed parameter systems and nonlinear GE-semigroup. Sci China Inf Sci 56(12):1\u201314","journal-title":"Sci China Inf Sci"},{"issue":"7","key":"3835_CR35","first-page":"079202","volume":"60","author":"FU Qin","year":"2017","unstructured":"Qin FU, Panpan GU, Xiangdong LI et al (2017) Iterative learning control approach for consensus of multi-agent systems with regular linear dynamics. Sci China 60(7):079202","journal-title":"Sci China"},{"issue":"1","key":"3835_CR36","first-page":"012204","volume":"60","author":"FU Qin","year":"2017","unstructured":"Qin FU, Panpan GU, Jianrong WU (2017) Iterative learning control for one-dimensional fourth order distributed parameter systems. Sci China 60(1):012204","journal-title":"Sci China"},{"issue":"9","key":"3835_CR37","first-page":"092206","volume":"59","author":"FU Qin","year":"2016","unstructured":"Qin FU, Weiguo GU, Panpan GU et al (2016) Feedback control for a class of second order hyperbolic distributed parameter systems. Sci China 59(9):092206","journal-title":"Sci China"},{"key":"3835_CR38","first-page":"821","volume":"34","author":"W Gu","year":"2016","unstructured":"Gu W, Fu Q, Wu J (2016) Iterative learning control for quasi-one-sided Lipschitz non-linear systems. IMA J Math Control Inf 34(3):821\u2013830","journal-title":"IMA J Math Control Inf"},{"key":"3835_CR39","unstructured":"Gu P, Fu Q, Li X (2016) Iterative learning control for switched linear parabolic systems in space W1, 2. In: Control and decision conference. IEEE"},{"issue":"2","key":"3835_CR40","first-page":"1","volume":"8","author":"J Wu","year":"2015","unstructured":"Wu J, Fu Q, Li Z (2015) H\u221e control via state observer feedback for the T\u2013S fuzzy generalized system. Int J Mach Learn Cybernet 8(2):1\u20138","journal-title":"Int J Mach Learn Cybernet"},{"issue":"7","key":"3835_CR41","doi-asserted-by":"publisher","first-page":"1123","DOI":"10.1109\/TSMC.2016.2557219","volume":"47","author":"C Chen","year":"2017","unstructured":"Chen C, Liu Z, Zhang Y et al (2017) Coordinated motion\/force control of multiarm robot with unknown sensor nonlinearity and manipulated object\u2019s uncertainty. IEEE Trans Syst Man Cybernet Syst 47(7):1123\u20131134","journal-title":"IEEE Trans Syst Man Cybernet Syst"},{"issue":"1","key":"3835_CR42","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.automatica.2010.08.019","volume":"3","author":"C Chen","year":"2016","unstructured":"Chen C, Liu Z, Zhang Y et al (2016) Adaptive control of MIMO mechanical systems with unknown actuator nonlinearities based on the Nussbaum gain approach. Automation 3(1):26\u201334","journal-title":"Automation"},{"issue":"1","key":"3835_CR43","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1109\/TFUZZ.2016.2551292","volume":"25","author":"G Lai","year":"2017","unstructured":"Lai G, Liu Z, Zhang Y et al (2017) Adaptive inversion-based fuzzy compensation control of uncertain pure-feedback systems with asymmetric actuator backlash. IEEE Trans Fuzzy Syst 25(1):141\u2013155","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"5","key":"3835_CR44","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1049\/ip-d.1993.0040","volume":"140","author":"Z Trzaska","year":"1993","unstructured":"Trzaska Z, Marszalek W (1993) Singular distributed parameter systems. IEE Proc D Control Theory Appl 140(5):305\u2013308","journal-title":"IEE Proc D Control Theory Appl"},{"key":"3835_CR45","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/BF02573287","volume":"39","author":"N Sauer","year":"1989","unstructured":"Sauer N, Singleton JE (1989) Evolution operators in empathy with a semigroup. Semigroup Forum 39:85\u201394","journal-title":"Semigroup Forum"},{"issue":"2","key":"3835_CR46","first-page":"138","volume":"25","author":"J Macionis","year":"1985","unstructured":"Macionis J (1985) Solvability of a degenerate differential equation with spectral parameter. Lith Math J 25(2):138\u2013142","journal-title":"Lith Math J"},{"issue":"2","key":"3835_CR47","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1007\/s11424-008-9109-8","volume":"21","author":"ZQ Ge","year":"2008","unstructured":"Ge ZQ, Zhu GT, Feng DX (2008) Degenerate semi-group methods for the exponential stability of the first order generalized distributed parameter systems. J Syst Sci Complex 21(2):260\u2013266","journal-title":"J Syst Sci Complex"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-018-3835-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-018-3835-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-018-3835-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,9]],"date-time":"2020-02-09T05:27:08Z","timestamp":1581226028000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-018-3835-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,2]]},"references-count":47,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["3835"],"URL":"https:\/\/doi.org\/10.1007\/s00521-018-3835-0","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,2]]},"assertion":[{"value":"22 July 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 October 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 November 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that there is no conflict of interests regarding the publication of this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}