Maximum likelihood gradient identification for multivariate equation-error moving average systems using the multi-innovation theory. (English) Zbl 1425.93293
Summary: For the multivariate equation-error moving average system, a multivariate maximum likelihood multi-innovation extended stochastic gradient (M-ML-MIESG) algorithm is delivered. The key is to decompose the system into several regressive identification subsystems according to the number of the system outputs. Then, a multivariate maximum likelihood extended stochastic gradient algorithm is presented to estimate the parameters of these subsystems. The M-ML-MIESG algorithm has higher parameter estimation accuracy than the multivariate extended stochastic gradient algorithm. The simulation examples indicate that the proposed methods work well.
MSC:
| 93E12 | Identification in stochastic control theory |
| 93E10 | Estimation and detection in stochastic control theory |
| 93C35 | Multivariable systems, multidimensional control systems |
Keywords:
gradient identification; maximum likelihood; multi-innovation; multivariate system; parameter estimationReferences:
| [1] | XuL. A proportional differential control method for a time‐delay system using the Taylor expansion approximation. Appl Math Comput. 2014;236:391‐399. · Zbl 1334.93125 |
| [2] | XuL. Application of the Newton iteration algorithm to the parameter estimation for dynamical systems. J Comput Appl Math. 2015;288:33‐43. · Zbl 1314.93062 |
| [3] | XuL, ChenL, XiongW. Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration. Nonlinear Dynamics. 2015;79(3):2155‐2163. |
| [4] | XuL. The damping iterative parameter identification method for dynamical systems based on the sine signal measurement. Signal Processing. 2016;120:660‐667. |
| [5] | XuL. The parameter estimation algorithms based on the dynamical response measurement data. Adv Mech Eng. 2017;9(11):1‐12. https://doi.org/10.1177/1687814017730003 · doi:10.1177/1687814017730003 |
| [6] | XuL, XiongW, 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. |
| [7] | ChenG‐Y, GanM, ChenCLP, LiHX. A regularized variable projection algorithm for separable nonlinear least‐squares problems. IEEE Trans Autom Control. 2019;64(2):526‐537. · Zbl 1482.93717 |
| [8] | ChenG‐Y, GanM, DingF, ChenCLP. Modified Gram‐Schmidt method‐based variable projection algorithm for separable nonlinear models. IEEE Trans Neural Netw Learn Syst. 2019. https://doi.org/10.1109/TNNLS.2018.2884909 · doi:10.1109/TNNLS.2018.2884909 |
| [9] | GanM, ChenCLP, ChenGY, ChenL. On some separated algorithms for separable nonlinear least squares problems. IEEE Trans Cybern. 2018;48(10):2866‐2874. |
| [10] | QianJH, LopsM, ZhengL, WangXD, HeZS. Joint system design for coexistence of MIMO radar and MIMO communication. IEEE Trans Signal Process. 2018;66(13):3504‐3519. · Zbl 1415.94208 |
| [11] | PanJ, MaH, JiangX, DingW, DingF. Adaptive gradient‐based iterative algorithm for multivariate controlled autoregressive moving average systems using the data filtering technique. Complexity. 2018. Article ID 9598307. https://doi.org/10.1155/2018/9598307 · Zbl 1398.93348 · doi:10.1155/2018/9598307 |
| [12] | DingJ. The hierarchical iterative identification algorithm for multi‐input‐output‐error systems with autoregressive noise. Complexity. 2017;1‐11. Article ID 5292894. https://doi.org/10.1155/2017/5292894 · Zbl 1377.93164 · doi:10.1155/2017/5292894 |
| [13] | LiDP, LiDJ, LiuYJ, TongSC, ChenCLP. Approximation‐based adaptive neural tracking control of nonlinear MIMO unknown time‐varying delay systems with full state constraints. IEEE Trans Cybern. 2017;47(10):3100‐3109. |
| [14] | SalhiH, KamounS. A recursive parametric estimation algorithm of multivariable nonlinear systems described by Hammerstein mathematical models. Appl Math Model. 2015;39(16):4951‐4962. · Zbl 1443.93016 |
| [15] | GaoZ‐K, FangP‐C, DingM‐S, JinN‐D. Multivariate weighted complex network analysis for characterizing nonlinear dynamic behavior in two‐phase flow. Exp Thermal Fluid Sci. 2015;60:157‐164. |
| [16] | HuangHL, ZhouHC, WangJ, ChangFR, MaM. A multivariate spatial model of crash frequency by transportation modes for urban intersections. Anal Methods Accid Res. 2017;14:10‐21. |
| [17] | DingJ, ChenJZ, LinJX, WangLJ. Particle filtering based parameter estimation for systems with output‐error type model structures. J Franklin Inst. 2019;356. https://doi.org/10.1016/j.jfranklin.2019.04.027 · Zbl 1415.93249 · doi:10.1016/j.jfranklin.2019.04.027 |
| [18] | LiuQY, DingF, XuL, YangEF. Partially coupled gradient estimation algorithm for multivariable equation‐error autoregressive moving average systems using the data filtering technique. IET Control Theory Appl. 2019;13(5):642‐650. · Zbl 1434.93103 |
| [19] | WangX, DingF. Convergence of the recursive identification algorithms for multivariate pseudo‐linear regressive systems. Int J Adapt Control Signal Process. 2015;30(6):824‐842. |
| [20] | LiuQ, DingF. Auxiliary model‐based recursive generalized least squares algorithm for multivariate output‐error autoregressive systems using the data filtering. Circuits Syst Signal Process. 2019;38(2):590‐610. |
| [21] | ZorziM. A new family of high‐resolution multivariate spectral estimators. IEEE Trans Autom Control. 2014;59(4):892‐904. · Zbl 1360.62467 |
| [22] | ZorziM. Multivariate spectral estimation based on the concept of optimal prediction. IEEE Trans Autom Control. 2015;60(6):1647‐1652. · Zbl 1360.62285 |
| [23] | UmenbergerJ, WagbergJ, ManchesterIR, SchönTB. Maximum likelihood identification of stable linear dynamical systems. Automatica. 2018;96:280‐292. · Zbl 1406.93362 |
| [24] | ChenX, ZhaoS, LiuF. Identification of time‐delay Markov jump autoregressive exogenous systems with expectation‐maximization algorithm. Int J Adapt Control Signal Process. 2017;31(12):1920‐1933. · Zbl 1383.93091 |
| [25] | JiaoJ, VenkatK, HanY, WeissmanT. Maximum likelihood estimation of functionals of discrete distributions. IEEE Trans Inf Theory. 2017;63(10):6774‐6798. · Zbl 1453.62432 |
| [26] | SöderströmT, SoveriniU. Errors‐in‐variables identification using maximum likelihood estimation in the frequency domain. Automatica. 2017;79:131‐143. · Zbl 1371.93210 |
| [27] | BaúburaM, ModugnoM. Maximum likelihood estimation of factor models on datasets with arbitrary pattern of missing data. J Appl Econ. 2014;29(1):133‐160. |
| [28] | ChenF, DingF. The filtering based maximum likelihood recursive least squares estimation for multiple‐input single‐output systems. Appl Math Model. 2016;40(3):2106‐2118. · Zbl 1452.62693 |
| [29] | ChangM‐X, ChangW‐Y. Maximum‐likelihood detection for MIMO systems based on differential metrics. IEEE Trans Signal Process. 2017;65(14):3718‐3732. · Zbl 1414.94772 |
| [30] | XuL, DingF. Parameter estimation algorithms for dynamical response signals based on the multi‐innovation theory and the hierarchical principle. IET Signal Processing. 2017;11(2):228‐237. |
| [31] | XuL, DingF. Recursive least squares and multi‐innovation stochastic gradient parameter estimation methods for signal modeling. Circuits Syst Signal Process. 2017;36(4):1735‐1753. · Zbl 1370.94286 |
| [32] | XuL, DingF, GuY, AlsaediA, HayatT. A multi‐innovation state and parameter estimation algorithm for a state space system with d‐step state‐delay. Signal Processing. 2017;140:97‐103. |
| [33] | PanJ, JiangX, WanX, DingW. A filtering based multi‐innovation extended stochastic gradient algorithm for multivariable control systems. Int J Control Autom Syst. 2017;15(3):1189‐1197. |
| [34] | DingF, WangX, MaoL, XuL. Joint state and multi‐innovation parameter estimation for time‐delay linear systems and its convergence based on the Kalman filtering. Digit Signal Process. 2017;62:211‐223. |
| [35] | ChengS, WeiY, ShengD, ChenY, WangY. Identification for Hammerstein nonlinear ARMAX systems based on multi‐innovation fractional order stochastic gradient. Signal Processing. 2018;142:1‐10. |
| [36] | LiuL, DingF, ZhuQ. Recursive identification for multivariate autoregressive equation‐error systems with autoregressive noise. Int J Syst Sci. 2018;49(13):2763‐2775. · Zbl 1482.93655 |
| [37] | CaoY, LuH, WenT. A safety computer system based on multi‐sensor data processing. Sensors. 2019;19(4). https://doi.org/10.3390/s19040818 · doi:10.3390/s19040818 |
| [38] | CaoY, ZhangY, WenT, LiP. Research on dynamic nonlinear input prediction of fault diagnosis based on fractional differential operator equation in high‐speed train control system. Chaos. 2019;29(1). Article ID 013130. https://doi.org/10.1063/1.5085397 · doi:10.1063/1.5085397 |
| [39] | CaoY, LiP, ZhangY. Parallel processing algorithm for railway signal fault diagnosis data based on cloud computing. Future Gener Comput Syst. 2018;88:279‐283. |
| [40] | CaoY, MaLC, XiaoS, ZhangS, XuW. Standard analysis for transfer delay in CTCS‐3. Chin J Electron. 2017;26(5):1057‐1063. |
| [41] | XuL, DingF. Parameter estimation for control systems based on impulse responses. Int J Control Autom Syst. 2017;15(6):2471‐2479. |
| [42] | DingF, LiuPX, LiuG. Gradient based and least‐squares based iterative identification methods for OE and OEMA systems. Digit Signal Process. 2010;20(3):664‐677. |
| [43] | DingF. Decomposition based fast least squares algorithm for output error systems. Signal Processing. 2013;93(5):1235‐1242. |
| [44] | DingF. Two‐stage least squares based iterative estimation algorithm for CARARMA system modeling. Appl Math Model. 2013;37(7):4798‐4808. · Zbl 1438.93228 |
| [45] | GuY, ChouY, LiuJ, JiY. Moving horizon estimation for multirate systems with time‐varying time‐delays. J Franklin Inst. 2019;356(4):2325‐2345. · Zbl 1409.93064 |
| [46] | GeZ, DingF, XuL, AlsaediA, HayatT. Gradient‐based iterative identification method for multivariate equation‐error autoregressive moving average systems using the decomposition technique. J Franklin Inst. 2019;356(3):1658‐1676. · Zbl 1406.93358 |
| [47] | ZhangX, DingF, AlsaadiFE, HayatT. Recursive parameter identification of the dynamical models for bilinear state space systems. Nonlinear Dynamics. 2017;89(4):2415‐2429. · Zbl 1377.93062 |
| [48] | ZhangX, XuL, DingF, HayatT. Combined state and parameter estimation for a bilinear state space system with moving average noise. J Franklin Inst. 2018;355(6):3079‐3103. · Zbl 1395.93174 |
| [49] | ZhangX, DingF, XuL, YangE. State filtering‐based least squares parameter estimation for bilinear systems using the hierarchical identification principle. IET Control Theory Appl. 2018;12(12):1704‐1713. |
| [50] | LiuS, DingF, XuL, HayatT. Hierarchical principle‐based iterative parameter estimation algorithm for dual‐frequency signals. Circuits Syst Signal Process. 2019;1‐18. https://doi.org/10.1007/s00034-018-1015-1 · doi:10.1007/s00034-018-1015-1 |
| [51] | XuH, DingF, YangE. Modeling a nonlinear process using the exponential autoregressive time series model. Nonlinear Dynamics. 2019;95(3):2079‐2092. https://doi.org/10.1007/s11071-018-4677-0 · Zbl 1432.37109 · doi:10.1007/s11071-018-4677-0 |
| [52] | WenY, YinC. Solution of Hamilton‐Jacobi‐Bellman equation in optimal reinsurance strategy under dynamic VaR constraint. J Funct Spaces. 2019. Article ID 6750892. https://doi.org/10.1155/2019/6750892 · Zbl 1411.91323 · doi:10.1155/2019/6750892 |
| [53] | TianX, NiuH. A bi‐objective model with sequential search algorithm for optimizing network‐wide train timetables. Comput Ind Eng. 2019;127:1259‐1272. |
| [54] | YangF, ZhangP, LiX‐X. The truncation method for the Cauchy problem of the inhomogeneous Helmholtz equation. Applicable Analysis. 2019;98(5):991‐1004. · Zbl 1409.35233 |
| [55] | SunZ‐Y, ZhangD, MengQ, ChenC‐C. Feedback stabilization of time‐delay nonlinear systems with continuous time‐varying output function. Int J Syst Sci. 2019;50(2):244‐255. · Zbl 1482.93479 |
| [56] | MaFY, YinYK, LiM. Start‐up process modelling of sediment microbial fuel cells based on data driven. Math Probl Eng. 2019. Article ID 7403732. https://doi.org/10.1155/2019/7403732 · doi:10.1155/2019/7403732 |
| [57] | ZhaoN, LiuR, ChenY, et al. Contract design for relay incentive mechanism under dual asymmetric information in cooperative networks. Wirel Netw. 2018;24(8):3029‐3044. |
| [58] | WuM, LiX, LiuC, et al. Robust global motion estimation for video security based on improved k‐means clustering. J Ambient Intell Humaniz Comput. 2019;10(2):439‐448. |
| [59] | WanX, WuH, QiaoF, et al. Electrocardiogram baseline wander suppression based on the combination of morphological and wavelet transformation based filtering. Comput Math Methods Med. 2019. Article ID 7196156. https://doi.org/10.1155/2019/7196156 · doi:10.1155/2019/7196156 |
| [60] | WangTZ, DongJJ, XieT, DialloD, BenbouzidM. A self‐learning fault diagnosis strategy based on multi‐model fusion. Information. 2019;10(3), Article Number: 116. https://doi.org/10.3390/info10030116 · doi:10.3390/info10030116 |
| [61] | ZhanX‐S, ChengL‐L, WuJ, YangQ‐S, HanT. Optimal modified performance of MIMO networked control systems with multi‐parameter constraints. ISA Transactions. 2019;84(1):111‐117. |
| [62] | PanJ, LiW, ZhangH. 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. |
| [63] | ShaXY, XuZS, YinCC. Elliptical distribution-based weight-determining method for ordered weighted averaging operators. Int J Intell Syst. 2019;34(5):858‐877. |
| [64] | FengL, LiQX, LiYF. Imaging with 3‐D aperture synthesis radiometers. IEEE Trans Geoscience and Remote Sensing. 2019;57(4):2395‐2406. |
| [65] | FuB, OuyangCX, LiCS, WangJW, GulE. An improved mixed integer linear programming approach based on symmetry diminishing for unit commitment of hybrid power system. Energies. 2019;12(5). Article No. 833. https://doi.org/10.3390/en12050833 · doi:10.3390/en12050833 |
| [66] | ShiWX, LiuN, ZhouYM, CaoXA. Effects of postannealing on the characteristics and reliability of polyfluorene organic light‐emitting diodes. IEEE Trans Electron Devices. 2019;66(2):1057‐1062. |
| [67] | WuTZ, ShiX, LiaoL, ZhouCJ, ZhouH, SuYH. A capacity configuration control strategy to alleviate power fluctuation of hybrid energy storage system based on improved particle swarm optimization. Energies. 2019;12(4):1‐11. Article Number: 642. https://doi.org/10.3390/en12040642 · doi:10.3390/en12040642 |
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