×

Iterative parameter identification algorithms for the generalized time-varying system with a measurable disturbance vector. (English) Zbl 1527.93041

Summary: This article deals with the parameter identification of the generalized time-varying systems. The time-varying parameter vector can be expressed as a coefficient matrix multiplied by a measurable disturbance vector, the common identification methods cannot be used to estimate the parameters of the generalized time-varying systems directly. This motivates us to develop new iterative identification algorithms. The gradient-based iterative (GI) algorithm is proposed by means of the iterative technique. Moreover, a moving data window (MDW) is introduced, which can update the dynamical data by removing the oldest data and adding the newest measurement data. The MDW GI algorithm is proposed to improve the parameter estimation accuracy. The numerical simulation is provided and the simulation results show that the proposed identification methods are effective for the generalized time-varying systems.
{© 2021 John Wiley & Sons Ltd.}

MSC:

93B30 System identification
Full Text: DOI

References:

[1] DingJ, ChenLJ, CaoZX, GuoHH. Convergence analysis of the modified adaptive extended Kalman filter for the parameter estimation of a brushless DC motor. Int J Robust Nonlinear Control. 2021;31(16):7606‐7620. · Zbl 1527.93199
[2] DingF. Combined state and least squares parameter estimation algorithms for dynamic systems. Appl Math Model. 2014;38(1):403‐412. · Zbl 1449.93254
[3] PanJ, JiangX, WanXK, DingW. A filtering based multi‐innovation extended stochastic gradient algorithm for multivariable control systems. Int J Control Autom Syst. 2017;15(3):1189‐1197.
[4] DingF, ChenT. Combined parameter and output estimation of dual‐rate systems using an auxiliary model. Automatica. 2004;40(10):1739‐1748. · Zbl 1162.93376
[5] DingF, ChenT. Parameter estimation of dual‐rate stochastic systems by using an output error method. IEEE Trans Automat Contr. 2005;50(9):1436‐1441. · Zbl 1365.93480
[6] LiZJ, DingJ, LinJX. Discrete fractional order PID controller design for nonlinear systems. Int J Syst Sci. 2021;52(15):3206‐3213. · Zbl 1483.93201
[7] DingJ, CaoZX, ChenJZ, JiangGP. Weighted parameter estimation for Hammerstein nonlinear ARX systems. Circuits Syst Signal Process. 2020;39(4):2178‐2192. · Zbl 1508.93067
[8] FengL, DingJ, HanYY. Improved sliding mode based EKF for SOC estimation of lithium‐ion batteries. Ionics. 2020;26(6):2875‐2882.
[9] DingF, ShiY, ChenT. Auxiliary model‐based least‐squares identification methods for Hammerstein output‐error systems. Syst Control Lett. 2007;56(5):373‐380. · Zbl 1130.93055
[10] KangZ, JiY, LiuXM. Hierarchical recursive least squares algorithms for Hammerstein nonlinear autoregressive output‐error systems. Int J Adapt Control Signal Process. 2021;35(11):2276‐2295. · Zbl 07840777
[11] FanYM, LiuXM. Two‐stage auxiliary model gradient‐based iterative algorithm for the input nonlinear controlled autoregressive system with variable‐gain nonlinearity. Int J Robust Nonlinear Control. 2020;30(14):5492‐5509. · Zbl 1465.93041
[12] DingF. Hierarchical multi‐innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling. Appl Math Model. 2013;37(4):1694‐1704. · Zbl 1349.93391
[13] SongS, LimJS, BaekS, et al. Gauss Newton variable forgetting factor recursive least squares for time varying parameter tracking. Electron Lett. 2000;36(11):988‐990.
[14] LeungX, SoCF. Gradient‐based variable forgetting factor RLS algorithm in time‐varying environments. IEEE Trans Signal Process. 2005;53(8):3141‐3150. · Zbl 1373.62465
[15] PingX, YangS, XiaoY, et al. Interval state estimation‐based robust model predictive control for linear parameter varying systems. Int J Robust Nonlinear Control. 2021;31(15):7026‐7052. · Zbl 1527.93113
[16] LiSJ, ZhengYJ, LinZP. Recursive identification of time‐varying systems: self‐tuning and matrix RLS algorithms. Syst Control Lett. 2014;66:104‐110. · Zbl 1288.93088
[17] DongSJ, YuL, ZhangWA, et al. Control and filtering of discrete‐time LPV systems exploring statistical information of the time‐varying parameters. J Frankl Inst. 2020;357(7):3809‐3834.
[18] ZhouX, XieX, YueD, et al. Further studies on state estimation of discrete‐time nonlinear parameter varying systems based on a new multi‐instant switching observer. Int J Robust Nonlinear Control. 2020. doi:10.1002/rnc.5333 · Zbl 1527.93440
[19] JiaoM, WangDQ, QiuJL. GRU‐RNN based momentum optimized algorithm for SOC estimation. J Power Sources. 2020;459:228051.
[20] LiY, WeiHL, BillingsSA. Identification of time‐varying systems using multi‐wavelet basis functions. IEEE Trans Control Syst Technol. 2011;19(3):656‐663.
[21] JingSX. Identification of the ARX model with random impulse noise based on forgetting factor multi‐error information entropy. Circuits Syst Signal Process. 2022. doi:10.1007/s00034-021-01809-3 · Zbl 1509.93004
[22] JingSX, PanTH, ZhuQM. Identification of Wiener systems based on the variable forgetting factor multierror stochastic gradient and the key term separation. Int J Adapt Control Signal Process. 2021;35(12):2537‐2549. · Zbl 07840966
[23] JingSX. Multierror stochastic gradient algorithm for identification of a Hammerstein system with random noise and its application in the modeling of a continuous stirring tank reactor. Optim Control Appl Methods. 2022. doi:10.1002/oca.2760 · Zbl 1531.93052
[24] DingF, YangJB, XuYM. Least squares identification method of generalized time‐varying systems. J Tsinghua Univ. 2000;40(3):86‐89.
[25] JiY, KangZ. Three‐stage forgetting factor stochastic gradient parameter estimation methods for a class of nonlinear systems. Int J Robust Nonlinear Control. 2021;31(3):871‐987. · Zbl 1525.93438
[26] WangLJ, JiY, WanLJ, BuN. Hierarchical recursive generalized extended least squares estimation algorithms for a class of nonlinear stochastic systems with colored noise. J Franklin Inst. 2019;356(16):10102‐10122. · Zbl 1423.93371
[27] XuL, ShengJ. Separable multi‐innovation stochastic gradient estimation algorithm for the nonlinear dynamic responses of systems. Int J Adapt Control Signal Process. 2020;34(7):937‐954. · Zbl 1469.93111
[28] JiY, KangZ, LiuXM. The data filtering based multiple‐stage Levenberg‐Marquardt algorithm for Hammerstein nonlinear systems. Int J Robust Nonlinear Control. 2021;31(15):7007‐7025. · Zbl 1527.93457
[29] XuL, ChenFY, HayatT. Hierarchical recursive signal modeling for multi‐frequency signals based on discrete measured data. Int J Adapt Control Signal Process. 2021;35(5):676‐693. · Zbl 07839333
[30] LiuXM, FanYM. Maximum likelihood extended gradient‐based estimation algorithms for the input nonlinear controlled autoregressive moving average system with variable‐gain nonlinearity. Int J Robust Nonlinear Control. 2021;31(9):4017‐4036. · Zbl 1526.93264
[31] WangDQ, ZhangS, GanM, QiuJL. A novel EM identification method for Hammerstein systems with missing output data. IEEE Trans Ind Inf. 2020;16(4):2500‐2508.
[32] XuL, SongGL. A recursive parameter estimation algorithm for modeling signals with multi‐frequencies. Circuits Syst Signal Process. 2020;39(8):4198‐4224. · Zbl 1452.94026
[33] ZhouYH, ZhangX. Hierarchical estimation approach for RBF‐AR models with regression weights based on the increasing data length. IEEE Trans Circuits Syst II Express Briefs. 2021;68(12):3597‐3601.
[34] JiY, ZhangC, KangZ, YuT. Parameter estimation for block‐oriented nonlinear systems using the key term separation. Int J Robust Nonlinear Control. 2020;30(9):3727‐3752. · Zbl 1466.93161
[35] JiY, KangZ, ZhangC. Two‐stage gradient‐based recursive estimation for nonlinear models by using the data filtering. Int J Control Autom Syst. 2021;19(8):2706‐2715.
[36] XuL. Decomposition strategy‐based hierarchical least mean square algorithm for control systems from the impulse responses. Int J Syst Sci. 2021;52(9):1806‐1821. · Zbl 1483.93637
[37] ChenJ, LiuYJ. Interval error correction auxiliary model based gradient iterative algorithms for multirate ARX models. IEEE Trans Automat Contr. 2020;65(10):4385‐4392. · Zbl 1536.93949
[38] JingSX. Identification of an ARX model with impulse noise using a variable step size information gradient algorithm based on the kurtosis and minimum Renyi error entropy. Int J of Robust Nonlinear Control. 2022. doi:10.1002/rnc.5903 · Zbl 1527.93456
[39] LiuLJ, LiuHB, HayatT. Data filtering based maximum likelihood gradient estimation algorithms for a multivariate equation‐error system with ARMA noise. J Franklin Inst. 2020;357(9):5640‐5662. · Zbl 1441.93312
[40] DingF, LiuG, LiuXP. Parameter estimation with scarce measurements. Automatica. 2011;47(8):1646‐1655. · Zbl 1232.62043
[41] ZhouYH, ZhangX. Partially‐coupled nonlinear parameter optimization algorithm for a class of multivariate hybrid models. Appl Math Comput. 2022;414:126663. · Zbl 1510.93338
[42] LiMH, LiuXM. The filtering‐based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle. Int J Adapt Control Signal Process. 2019;33(7):1189‐1211. · Zbl 1425.93284
[43] LiMH, LiuXM. Maximum likelihood least squares based iterative estimation for a class of bilinear systems using the data filtering technique. Int J Control Autom Syst. 2020;18(6):1581‐1592.
[44] XuL. Separable multi‐innovation Newton iterative modeling algorithm for multi‐frequency signals based on the sliding measurement window. Circuits Syst Signal Process. 2022;41. doi:10.1007/s00034-021-01801-x · Zbl 1509.94036
[45] LiMH, LiuXM. Iterative identification methods for a class of bilinear systems by using the particle filtering technique. Int J Adapt Control Signal Process. 2021;35(11):2056‐2074. · Zbl 07840498
[46] DingF, LiuYJ, BaoB. Gradient based and least squares based iterative estimation algorithms for multi‐input multi‐output systems. Proc Inst Mech Eng I J Syst Control Eng. 2012;226(1):43‐55.
[47] LiMH, LiuXM. Maximum likelihood hierarchical least squares‐based iterative identification for dual‐rate stochastic systems. Int J Adapt Control Signal Process. 2021;35(2):240‐261. · Zbl 07839197
[48] JiY, JiangXK, WanLJ. Hierarchical least squares parameter estimation algorithm for two‐input Hammerstein finite impulse response systems. J Franklin Inst. 2020;357(8):5019‐5032. · Zbl 1437.93131
[49] ZhaoSY, ShmaliyYS, AhnCK. Iterative maximum likelihood FIR estimation of dynamic systems with improved robustness. IEEE/ASME Trans Mechatron. 2018;23(3):1467‐1476.
[50] WangJW, JiY, ZhangC. Iterative parameter and order identification for fractional‐order nonlinear finite impulse response systems using the key term separation. Int J Adapt Control Signal Process. 2021;35(8):1562‐1577. · Zbl 07840333
[51] WangDQ, FanQH, MaY. An interactive maximum likelihood estimation method for multivariable Hammerstein systems. J Franklin Inst. 2020;357:12986‐13005. · Zbl 1454.93285
[52] LiXD, LiP. Stability of time‐delay systems with impulsive control involving stabilizing delays. Automatica. 2021;124:109336. · Zbl 1461.93436
[53] XuL, XiongWL, AlsaediA, HayatT. Hierarchical parameter estimation for the frequency response based on the dynamical window data. Int J Control Autom Syst. 2018;16(4):1756‐1764.
[54] DingF, LiuG, LiuXP. Partially coupled stochastic gradient identification methods for non‐uniformly sampled systems. IEEE Trans Automat Contr. 2010;55(8):1976‐1981. · Zbl 1368.93121
[55] MaH, PanJ, DingW. Partially‐coupled least squares based iterative parameter estimation for multi‐variable output‐error‐like autoregressive moving average systems. IET Control Theory Appl. 2019;13(18):3040‐3051.
[56] PanJ, MaH, ShengJ. Recursive coupled projection algorithms for multivariable output‐error‐like systems with coloured noises. IET Signal Process. 2020;14(7):455‐466.
[57] DingJ, LiuG. Hierarchical least squares identification for linear SISO systems with dual‐rate sampled‐data. IEEE Trans Automat Contr. 2022;56(11):2677‐2683. · Zbl 1368.93744
[58] MaH, ZhangX, HayatT. Partially‐coupled gradient‐based iterative algorithms for multivariable output‐error‐like systems with autoregressive moving average noises. IET Control Theory Appl. 2020;14(17):2613‐2627. · Zbl 1542.93385
[59] ZhangX, YangEF. Highly computationally efficient state filter based on the delta operator. Int J Adapt Control Signal Process. 2019;33(6):875‐889. · Zbl 1425.93290
[60] ZhangX. Adaptive parameter estimation for a general dynamical system with unknown states. Int J Robust Nonlinear Control. 2020;30(4):1351‐1372. · Zbl 1465.93115
[61] DingF. Coupled‐least‐squares identification for multivariable systems. IET Control Theory Appl. 2013;7(1):68‐79.
[62] LiuYJ, ShiY. An efficient hierarchical identification method for general dual‐rate sampled‐data systems. Automatica. 2014;50(3):962‐970. · Zbl 1298.93227
[63] WangYJ. Novel data filtering based parameter identification for multiple‐input multiple‐output systems using the auxiliary model. Automatica. 2016;71:308‐313. · Zbl 1343.93087
[64] ZhangX, YangEF. State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors. Int J Adapt Control Signal Process. 2019;33(7):1157‐1173. · Zbl 1425.93278
[65] ZhangX, YangEF. State filtering‐based least squares parameter estimation for bilinear systems using the hierarchical identification principle. IET Control Theory Appl. 2018;12(12):1704‐1713.
[66] ZhangX, HayatT. Combined state and parameter estimation for a bilinear state space system with moving average noise. J Frankl Inst. 2018;355(6):3079‐3103. · Zbl 1395.93174
[67] ZhangX, HayatT. Recursive parameter identification of the dynamical models for bilinear state space systems. Nonlinear Dyn. 2017;89(4):2415‐2429. · Zbl 1377.93062
[68] LiXY, WangHL, WuBY. A stable and efficient technique for linear boundary value problems by applying kernel functions. Appl Numer Math. 2022;172:206‐214. · Zbl 1484.65170
[69] DongH, YinCC, DaiHS. Spectrally negative Levy risk model under Erlangized barrier strategy. J Comput Appl Math. 2019;351:101‐116. · Zbl 1419.91356
[70] ShaXY, XuZS, YinCC. Elliptical distribution‐based weight‐determining method for ordered weighted averaging operators. Int J Intell Syst. 2019;34(5):858‐877.
[71] YinCC, WenYZ. An extension of Paulsen‐Gjessing’s risk model with stochastic return on investments. Insur Math Econom. 2013;52(3):469‐476. · Zbl 1284.91281
[72] ZhaoYX, ChenP, YangHL. Optimal periodic dividend and capital injection problem for spectrally positive Levy processes. Insur Math Econom. 2017;74:135‐146. · Zbl 1394.91243
[73] ZhaoXH, DongH, DaiHS. On spectrally positive Levy risk processes with Parisian implementation delays in dividend payments. Stat Probab Lett. 2018;140:176‐184. · Zbl 1410.91297
[74] ZhaoYX, YinCC. The expected discounted penalty function under a renewal risk model with stochastic income. Appl Math Comput. 2012;218(10):6144‐6154. · Zbl 1242.60089
[75] PanJ, LiW, ZhangHP. Control algorithms of magnetic suspension systems based on the improved double exponential reaching law of sliding mode control. Int J Control Autom Syst. 2018;16(6):2878‐2887.
[76] ZhangX. Recursive parameter estimation methods and convergence analysis for a special class of nonlinear systems. Int J Robust Nonlinear Control. 2020;30(4):1373‐1393. · Zbl 1465.93218
[77] ZhangX. Recursive parameter estimation and its convergence for bilinear systems. IET Control Theory Appl. 2020;14(5):677‐688. · Zbl 07907139
[78] ZhangX. Hierarchical parameter and state estimation for bilinear systems. Int J Syst Sci. 2020;51(2):275‐290. · Zbl 1483.93677
[79] ZhangX, LiuQY, HayatT. Recursive identification of bilinear time‐delay systems through the redundant rule. J Frankl Inst. 2020;357(1):726‐747. · Zbl 1429.93401
[80] ZhaoZY, ZhouYQ, WangXY, WangZY, BaiYT. Water quality evolution mechanism modeling and health risk assessment based on stochastic hybrid dynamic systems. Expert Syst Appl. 2022.
[81] ChenGY, GanM, ChenCLP, LiHX. A regularized variable projection algorithm for separable nonlinear least‐squares problems. IEEE Trans Automat Contr. 2019;64(2):526‐537. · Zbl 1482.93717
[82] XuL. Auxiliary model multiinnovation stochastic gradient parameter estimation methods for nonlinear sandwich systems. Int J Robust Nonlinear Control. 2021;31(1):148‐165. · Zbl 1525.93043
[83] DingF, LiuXG, ChuJ. Gradient‐based and least‐squares‐based iterative algorithms for Hammerstein systems using the hierarchical identification principle. IET Control Theory Appl. 2013;7(2):176‐184.
[84] HouJ, ChenFW, LiPH, ZhuZQ. Gray‐box parsimonious subspace identification of Hammerstein‐type systems. IEEE Trans Ind Electron. 2021;68(10):9941‐9951.
[85] XuL. Separable Newton recursive estimation method through system responses based on dynamically discrete measurements with increasing data length. Int J Control Autom Syst. 2022;20.
[86] KongJL, WangHX, WangXY, et al. Multi‐stream hybrid architecture based on cross‐level fusion strategy for fine‐grained crop species recognition in precision agriculture. Comput Electron Agric. 2021;185, 106134.
[87] ZhengYY, KongJL, JinXB, et al. CropDeep: the crop vision dataset for deep‐learning‐based classification and detection in precision agriculture. Sensors. 2019;19(5):1058.
[88] BuN, PangJX, DengM. Robust fault tolerant tracking control for the multi‐joint manipulator based on operator theory. J Frankl Inst. 2020;357(5):2696‐2714. · Zbl 1451.93068
[89] DingJL, ZhangWH. Finite‐time adaptive control for nonlinear systems with uncertain parameters based on the command filters. Int J Adapt Control Signal Process. 2021;35(9):1754‐1767. · Zbl 07840344
[90] MaP, WangL. Filtering‐based recursive least squares estimation approaches for multivariate equation‐error systems by using the multi‐innovation theory. Int J Adapt Control Signal Process. 2021;35(9):1898‐1915. · Zbl 1536.93999
[91] MaoYW, LiuS, LiuJF. Robust economic model predictive control of nonlinear networked control systems with communication delays. Int J Adapt Control Signal Process. 2020;34(5):614‐637. · Zbl 1467.93095
[92] ChenJ, HuangB, GanM, ChenCLP. A novel reduced‐order algorithm for rational models based on Arnoldi process and Krylov subspace. Automatica. 2021;129, 109663. · Zbl 1478.93081
[93] ChenJ, ZhuQM, LiuYJ. Modified Kalman filtering based multi‐step‐length gradient iterative algorithm for ARX models with random missing outputs. Automatica. 2020;118, 109034. · Zbl 1447.93350
[94] ChenJ, ShenQY, MaJX, LiuYJ. Stochastic average gradient algorithm for multirate FIR models with varying time delays using self‐organizing maps. Int J Adapt Control Signal Process. 2020;34(7):955‐970. · Zbl 1469.93108
[95] XiongW, JiaX, YangD, AiM, LiL, WangS. DP‐LinkNet: a convolutional network for historical document image binarization. KSII Trans Internet Inf Syst. 2021;15(5):1778‐1797.
[96] XiongW, ZhouL, YueL, LiL, WangS. An enhanced binarization framework for degraded historical document images. EURASIP J Image Video Process. 2021;2021, 13.
[97] ChangC, WangQY, JiangJC, WuTZ. Lithium‐ion battery state of health estimation using the incremental capacity and wavelet neural networks with genetic algorithm. J Energy Storage. 2021;38, 102570.
[98] ChangC, WuYT, JiangJC, et al. Prognostics of the state of health for lithium‐ion battery packs in energy storage applications. Energy. 2022;Part B:239, 122189.
[99] ZhaoG, GaoTH, WangYD, et al. Optimal sizing of isolated microgrid containing photovoltaic/photothermal/wind/diesel/battery. Int J Photoenergy. 2021;2021:5566597.
[100] WangXG, ZhaoM, ZhouY, WanZW, XuW. Design and analysis for multi‐disc coreless axial‐flux permanent‐magnet synchronous machine. IEEE Transn Appl Superconduct. 2021;31(8):5203804.
[101] WangXG, WanZW, TangL, XuW, ZhaoM. Electromagnetic performance analysis of an axial flux hybrid excitation motor for HEV drives. IEEE Trans Appl Superconduct. 2021;31(8):5205605.
[102] LiM, XuG, LaiQ, ChenJ. A chaotic strategy‐based quadratic opposition‐based learning adaptive variable‐speed whale optimization algorithm. Math Comput Simul. 2022;193:71‐99. · Zbl 1540.90308
[103] CaoY, SunYK, XieG, et al. A sound‐based fault diagnosis method for railway point machines based on two‐stage feature selection strategy and ensemble classifier. IEEE Trans Intell Transp Syst. 2022. doi:10.1109/TITS.2021.3109632
[104] CaoY, MaLC, XiaoS, et al. Standard analysis for transfer delay in CTCS‐3. Chin J Electron. 2017;26(5):1057‐1063.
[105] CaoY, WenJK, MaLC. Tracking and collision avoidance of virtual coupling train control system. Alex Eng J. 2021;60(2):2115‐2125.
[106] HaoLL, ZhanXS, WuJ. Bipartite finite time and fixed time output consensus of heterogeneous multiagent systems under state feedback control. IEEE Trans Circuits Syst II Express Briefs. 2021;68(6):2067‐2071.
[107] SuS, TangT, XunJ, et al. Design of running grades for energy‐efficient train regulation: a case study for Beijing Yizhuang line. IEEE Intell Transp Syst Mag. 2021;13(2):189‐200.
[108] SunY, CaoY, XieG, WenT. Sound based fault diagnosis for RPMs based on multi‐scale fractional permutation entropy and two‐scale algorithm. IEEE Trans Veh Technol. 2021;70(11):11184‐11192.
[109] CaoY, WangZ, LiuF, et al. Bio‐inspired speed curve optimization and sliding mode tracking control for subway trains. IEEE Trans Veh Technol. 2019;68(7):6331‐6342.
[110] CaoY, SunYK, XieG, et al. Fault diagnosis of train plug door based on a hybrid criterion for IMFs selection and fractional wavelet package energy entropy. IEEE Trans Veh Technol. 2019;68(8):7544‐7551.
[111] SuS, WangXK, CaoY, YinJT. An energy‐efficient train operation approach by integrating the metro timetabling and eco‐driving. IEEE Trans Intell Transp Syst. 2020;21(10):4252‐4268.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.