Convergence of the auxiliary model-based multi-innovation generalized extended stochastic gradient algorithm for Box–Jenkins systems
This paper focuses on the parameter estimation problem of Box–Jenkins systems. Using the multi-innovation identification theory, an auxiliary model-based multi-innovation generalized extended stochastic gradient algorithm is derived. The convergence of the proposed algorithm is analyzed based on the...
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| Vydáno v: | Nonlinear dynamics Ročník 82; číslo 1-2; s. 269 - 280 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Springer Netherlands
01.10.2015
Springer Nature B.V |
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| ISSN: | 0924-090X, 1573-269X |
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| Abstract | This paper focuses on the parameter estimation problem of Box–Jenkins systems. Using the multi-innovation identification theory, an auxiliary model-based multi-innovation generalized extended stochastic gradient algorithm is derived. The convergence of the proposed algorithm is analyzed based on the stochastic martingale theory. It is proved that the parameter estimation errors converge to zero under persistent excitation conditions. Two simulation examples are provided to confirm the convergence results. |
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| AbstractList | This paper focuses on the parameter estimation problem of Box–Jenkins systems. Using the multi-innovation identification theory, an auxiliary model-based multi-innovation generalized extended stochastic gradient algorithm is derived. The convergence of the proposed algorithm is analyzed based on the stochastic martingale theory. It is proved that the parameter estimation errors converge to zero under persistent excitation conditions. Two simulation examples are provided to confirm the convergence results. |
| Author | Ding, Feng Wang, Xuehai |
| Author_xml | – sequence: 1 givenname: Xuehai surname: Wang fullname: Wang, Xuehai organization: Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, School of Mathematics and Physics, Henan University of Urban Construction – sequence: 2 givenname: Feng surname: Ding fullname: Ding, Feng email: fding@jiangnan.edu.cn organization: Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University |
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| CitedBy_id | crossref_primary_10_1007_s00034_015_0164_8 crossref_primary_10_1016_j_jfranklin_2019_04_009 crossref_primary_10_1109_LSP_2018_2864609 crossref_primary_10_1016_j_dsp_2018_09_006 crossref_primary_10_1016_j_ifacol_2017_08_2436 crossref_primary_10_1007_s11071_016_3054_0 crossref_primary_10_1007_s00034_024_02777_0 crossref_primary_10_1016_j_dsp_2016_05_005 crossref_primary_10_1007_s00034_015_0210_6 crossref_primary_10_1177_1687814017730003 crossref_primary_10_1177_0142331216674772 crossref_primary_10_1007_s12555_016_0081_z crossref_primary_10_1016_j_jfranklin_2015_08_018 crossref_primary_10_3390_a10030084 crossref_primary_10_1016_j_jfranklin_2020_02_009 crossref_primary_10_1016_j_jprocont_2016_11_007 crossref_primary_10_1007_s00034_016_0368_6 crossref_primary_10_1049_iet_cta_2015_1056 crossref_primary_10_1016_j_ifacol_2018_09_422 crossref_primary_10_1049_iet_cta_2018_6413 crossref_primary_10_1016_j_dsp_2016_11_010 crossref_primary_10_1016_j_apm_2020_08_076 crossref_primary_10_1016_j_jfranklin_2016_12_024 |
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| Keywords | Box–Jenkins system Recursive identification Gradient search Parameter estimation Performance analysis |
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| References_xml | – reference: PintelonRSchoukensJRolainYBox–Jenkins continuous-time modelingAutomatica2000367983991182969510.1016/S0005-1098(00)00002-90997.93005 – reference: LiuYJWangDQLeast squares based iterative algorithms for identifying Box–Jenkins models with finite measurement dataDigit. Signal Process.20102051458146710.1016/j.dsp.2010.01.004 – reference: LiuYBaiEWIterative identification of Hammerstein systemsAutomatica2007432346354228184010.1016/j.automatica.2006.09.0041111.93013 – reference: VörösJRecursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zonesIEEE Trans. Autom. Control200348122203220610.1109/TAC.2003.820146 – reference: DingFState filtering and parameter identification for state space systems with scarce measurementsSignal Process.201410436938010.1016/j.sigpro.2014.03.031 – reference: DingFWangYJDingJRecursive least squares parameter estimation algorithms for systems with colored noise using the filtering technique and the auxiliary modelDigit. Signal Process.20153710010810.1016/j.dsp.2014.10.005 – reference: HuYBLiuBLZhouQYangCRecursive extended least squares parameter estimation for Wiener nonlinear systems with moving average noisesCircuits Syst. Signal Process.2014332655664316246010.1007/s00034-013-9652-x – reference: WangXHDingFPerformance analysis of the recursive parameter estimation algorithms for multivariable Box–Jenkins systemsJ. Franklin Inst. Eng. Appl. Math.20143511047494764325914110.1016/j.jfranklin.2014.07.004 – reference: ZhuDQHuangHYangSXDynamic task assignment and path planning of multi-AUV system based on an improved self-organizing map and velocity synthesis method in three-dimensional underwater workspaceIEEE Trans. Cybern.201343250451410.1109/TSMCB.2012.2210212 – reference: DingFSystem Identification—Performances Analysis for Identification Methods2014BeijingScience Press – reference: ZhangYYangHZBias compensation recursive least squares identification for output error systems with colored noisesActa Automat. Sin.20073310105310601164.93415 – reference: Ding, F., Chen, T.: Performance analysis of multi-innovation gradient type identification methods. Automatica 43(1), 1–14 (2007) – reference: XieLYangHZInteractive parameter estimation for output error moving average systemsTrans. Inst. Meas. 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| SubjectTerms | Algorithms Automotive Engineering Classical Mechanics Computer simulation Control Convergence Dynamical Systems Economic models Engineering Estimating techniques Innovations Martingales Mathematical models Mechanical Engineering Original Paper Parameter estimation Parameter identification Vibration |
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| Title | Convergence of the auxiliary model-based multi-innovation generalized extended stochastic gradient algorithm for Box–Jenkins systems |
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