{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:59:48Z","timestamp":1777705188351,"version":"3.51.4"},"reference-count":30,"publisher":"SAGE Publications","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,9,15]]},"abstract":"<jats:p>\u00a0The combination of machine learning and artificial intelligent has already proved its potential in achieving remarkable results for modeling unknown systems. These techniques commonly use enough data samples to train and optimize their architectures. In the present era, with the availability of enough storage and computation power, the machine learning based data-driven system modeling approaches are getting popular as they do not interrupt the normal system operations and work solely on collected data. This work proposes a data-driven parametric neural network technique for modeling time-delayed systems, which is demanding but challenging area of research and comes under nonlinear optimization problem. The key contribution of this work is the inclusion of an extended B-polynomial into the network structure for estimating time-delayed first and second order system models. These type of models extensively used for addressing simulations, predictions, controlling and monitoring related issues. Also, an adaptive learning based convergence of the proposed algorithm is proved with the help of the Lyapunov stability theory. The proposed algorithm compared with existing techniques on some well-known example problems. A real practical system plant is also included for validating the proposed concept.<\/jats:p>","DOI":"10.3233\/jifs-210580","type":"journal-article","created":{"date-parts":[[2021,7,23]],"date-time":"2021-07-23T10:58:51Z","timestamp":1627037931000},"page":"3277-3288","source":"Crossref","is-referenced-by-count":8,"title":["Extended B-polynomial neural network for time-delayed system modeling using sampled data"],"prefix":"10.1177","volume":"41","author":[{"given":"Sudeep","family":"Sharma","sequence":"first","affiliation":[{"name":"Department of Electronics and Communication, PDPMIIITDM, Jabalpur, Madhya Pradesh, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Prabin K.","family":"Padhy","sequence":"additional","affiliation":[{"name":"Department of Electronics and Communication, PDPMIIITDM, Jabalpur, Madhya Pradesh, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-210580_ref1","doi-asserted-by":"crossref","unstructured":"Pintelon R. and Schoukens J. , System identification: a frequency domain approach, John Wiley & Sons (2012).","DOI":"10.1002\/9781118287422"},{"issue":"3","key":"10.3233\/JIFS-210580_ref2","doi-asserted-by":"crossref","first-page":"167","DOI":"10.3233\/IFS-1997-5301","article-title":"Identification of Discrete-Time DynamicalSystems Via Recurrent Fuzzy Models","volume":"5","author":"John","year":"1997","journal-title":"Journal of Intelligent andFuzzy Systems"},{"issue":"4","key":"10.3233\/JIFS-210580_ref3","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1007\/s40010-017-0357-6","article-title":"Estimation of first and second orderprocess model parameters","volume":"88","author":"Bajarangbali","year":"2018","journal-title":"Proceedings of the National Academyof Sciences, India Section A: Physical Sciences"},{"issue":"3,4","key":"10.3233\/JIFS-210580_ref4","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1155\/2008\/512590","article-title":"Simple Models forthe Dynamic Modeling of Rotating Tires","volume":"15","author":"Delamotte","year":"2008","journal-title":"Shock and Vibration"},{"key":"10.3233\/JIFS-210580_ref5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/ACCESS.2020.2985132","article-title":"A novel iterative system identificationand modeling scheme with simultaneous time-delay and rationalparameter estimation","volume":"8","author":"Sharma","year":"2020","journal-title":"IEEE Access"},{"key":"10.3233\/JIFS-210580_ref7","doi-asserted-by":"crossref","first-page":"109419","DOI":"10.1016\/j.automatica.2020.109419","article-title":"Universal adaptive control strategiesfor stochastic nonlinear time-delay systems with odd rationalpowers","volume":"125","author":"Liu","year":"2021","journal-title":"Automatica"},{"key":"10.3233\/JIFS-210580_ref8","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.automatica.2017.11.023","article-title":"Universal strategies to explicit adaptivecontrol of nonlinear time-delay systems with different structures","volume":"89","author":"Liu","year":"2018","journal-title":"Automatica"},{"key":"10.3233\/JIFS-210580_ref11","first-page":"157","article-title":"Identification ofprocess transfer function parameters in event-based pi controlloops","volume":"75","author":"Snchez","year":"2018","journal-title":"Automatica"},{"issue":"7","key":"10.3233\/JIFS-210580_ref12","doi-asserted-by":"crossref","first-page":"1530","DOI":"10.1021\/ie00055a019","article-title":"An improved autotuneidentification method","volume":"30","author":"Li","year":"1991","journal-title":"Ind Eng Chem Res"},{"issue":"5","key":"10.3233\/JIFS-210580_ref13","doi-asserted-by":"crossref","first-page":"790","DOI":"10.1016\/j.compchemeng.2005.12.013","article-title":"Relay based PIPD design for stable andunstable FOPDT processes","volume":"30","author":"Padhy","year":"2006","journal-title":"Computers & Chemical Engineering"},{"key":"10.3233\/JIFS-210580_ref14","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.isatra.2015.03.015","article-title":"Identification of non-minimum phaseprocesses with time delay in the presence of measurement noise","volume":"57","author":"Bajarangbali","year":"2015","journal-title":"ISA Transactions"},{"key":"10.3233\/JIFS-210580_ref15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ins.2019.04.027","article-title":"Online policyiterative-based H \u00a5 optimization algorithm for a class of nonlinearsystems","volume":"495","author":"He","year":"2019","journal-title":"Information Sciences"},{"issue":"3","key":"10.3233\/JIFS-210580_ref16","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1109\/TNN.2004.826206","article-title":"Identification and control of a nonlineardiscrete-time system based on its linearization: a unifiedframework","volume":"15","author":"Chen","year":"2004","journal-title":"IEEE Transactions on Neural Networks"},{"issue":"3","key":"10.3233\/JIFS-210580_ref17","first-page":"6856","article-title":"Linear Recurrent Neural Network foropen and closed-loop consistent identification of LPV models","volume":"28","author":"Abbas","year":"2010","journal-title":"IEEE Conference on Decision and Control (CDC)"},{"issue":"2","key":"10.3233\/JIFS-210580_ref18","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1109\/TNNLS.2019.2905715","article-title":"Adaptive OptimalControl for a Class of Nonlinear Systems: The Online PolicyIteration Approach","volume":"31","author":"He","year":"2020","journal-title":"IEEE Transactions on Neural Networks andLearning Systems"},{"issue":"11","key":"10.3233\/JIFS-210580_ref19","doi-asserted-by":"crossref","first-page":"2004","DOI":"10.1109\/TAC.2003.819287","article-title":"Adaptive neural network control ofnonlinear systems with unknown time delays","volume":"48","author":"Ge","year":"2003","journal-title":"IEEE Transactionson Automatic Control"},{"issue":"3","key":"10.3233\/JIFS-210580_ref20","doi-asserted-by":"crossref","first-page":"221","DOI":"10.3233\/IFS-1994-2302","article-title":"On the Dynamics and Applications of a DiscreteTime Binary Neural Network with Time Delay","volume":"2","author":"Gardella","year":"1994","journal-title":"Journal ofIntelligent and Fuzzy Systems"},{"key":"10.3233\/JIFS-210580_ref21","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.asoc.2016.05.012","article-title":"Parametric system identification using neuralnetworks","volume":"47","author":"Tutunji","year":"2016","journal-title":"Applied Soft Computing"},{"issue":"1","key":"10.3233\/JIFS-210580_ref23","doi-asserted-by":"crossref","first-page":"59","DOI":"10.3233\/IDA-2001-5105","article-title":"Parameter extraction byparallel neural networks","volume":"5","author":"Wong","year":"2001","journal-title":"Intelligent Data Analysis"},{"issue":"4","key":"10.3233\/JIFS-210580_ref24","doi-asserted-by":"crossref","first-page":"2479","DOI":"10.3233\/JIFS-171947","article-title":"Dynamic structural neuralnetwork","volume":"34","author":"Giap","year":"2018","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"issue":"5","key":"10.3233\/JIFS-210580_ref25","doi-asserted-by":"crossref","first-page":"6145","DOI":"10.3233\/JIFS-189085","article-title":"Artificial Neural Networks andAdaptive Neuro-fuzzy Inference Systems for Parameter Identificationof Dynamic Systems","volume":"39","author":"Vatankhah","year":"2020","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"issue":"4","key":"10.3233\/JIFS-210580_ref26","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1016\/S0019-0578(07)60007-X","article-title":"On-line lower-order modeling vianeural networks","volume":"42","author":"Ho","year":"2003","journal-title":"ISA Transactions"},{"issue":"5","key":"10.3233\/JIFS-210580_ref27","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.1177\/0142331216688249","article-title":"Weighted parametric model identificationof induction motors with variable loads using FNN structure andNN2TF algorithm","volume":"40","author":"Tutunji","year":"2018","journal-title":"Transactions of the Institute of Measurementand Control"},{"issue":"3","key":"10.3233\/JIFS-210580_ref28","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1109\/10.554763","article-title":"Linear and nonlinear ARMA model parameterestimation using an artificial neural network","volume":"44","author":"Chon","year":"1997","journal-title":"IEEETransactions on Biomedical Engineering"},{"issue":"3","key":"10.3233\/JIFS-210580_ref29","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1191\/0142331206tim171oa","article-title":"A Novel Linear Recurrent NeuralNetwork for Multivariable System Identification","volume":"28","author":"Fei","year":"2006","journal-title":"Transactionsof the Institute of Measurement and Control"},{"issue":"6","key":"10.3233\/JIFS-210580_ref30","doi-asserted-by":"crossref","first-page":"989","DOI":"10.1109\/72.329697","article-title":"Training feedforward networks with theMarquardt algorithm","volume":"5","author":"Hagan","year":"1994","journal-title":"IEEE Transactions on Neural Networks"},{"issue":"1","key":"10.3233\/JIFS-210580_ref31","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/BF01593790","article-title":"Restart procedures for the conjugate gradient method","volume":"12","author":"Powell","year":"1977","journal-title":"Mathematical Programming"},{"issue":"2","key":"10.3233\/JIFS-210580_ref34","doi-asserted-by":"crossref","first-page":"1900","DOI":"10.1109\/TNNLS.2014.2361267","article-title":"Training recurrent neural networks with the Levenberg Marquardt algorithm foroptimal control of a grid-connected converter","volume":"26","author":"Fu","year":"2015","journal-title":"IEEETransactions on Neural Networks and Learning Systems"},{"issue":"1","key":"10.3233\/JIFS-210580_ref35","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1002\/rnc.5271","article-title":"New results on explicit adaptivecontrol design for nonlinear systems with polynomial conditions","volume":"31","author":"Liu","year":"2021","journal-title":"International Journal of Robust and Nonlinear Control"},{"issue":"2","key":"10.3233\/JIFS-210580_ref36","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1109\/TSMC.2018.2884491","article-title":"Robust H\u00a5 Sliding Mode Controller Designof a Class of Time-Delayed Discrete Conic-Type Nonlinear Systems","volume":"51","author":"He","year":"2021","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics: Systems"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-210580","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:43:09Z","timestamp":1777455789000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-210580"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,15]]},"references-count":30,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.3233\/jifs-210580","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,15]]}}}