Filtering-based multistage recursive identification algorithm for an input nonlinear output-error autoregressive system by using the key term separation technique. (English) Zbl 1368.93724
Summary: This paper derives a data filtering-based two-stage stochastic gradient algorithm and a data filtering-based multistage recursive least-squares algorithm for input nonlinear output-error autoregressive systems (i.e., Hammerstein systems). The output of the system is expressed as a linear combination of all system parameters based on the key term separation technique. The basic idea of the proposed algorithm is to filter the input-output data and to separate the parameter vector into several vectors and to interactively identify each parameter vector. The data filtering-based two-stage stochastic gradient algorithm has higher convergence rate than the stochastic gradient algorithm. Compared with the recursive generalized least-squares algorithm, the dimensions of the involved covariance matrices in the data filtering-based multistage recursive least-squares algorithm become small, and thus the data filtering-based multistage recursive least-squares algorithm has a higher computational efficiency. The numerical simulation results indicate that the proposed algorithms are effective.
MSC:
| 93E11 | Filtering in stochastic control theory |
| 93E25 | Computational methods in stochastic control (MSC2010) |
| 93E12 | Identification in stochastic control theory |
| 93C10 | Nonlinear systems in control theory |
Keywords:
filtering technique; nonlinear model; key term separation; decomposition; recursive identificationReferences:
| [1] | E.W. Bai, An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems. Automatica 34(3), 333-338 (1998) · Zbl 0915.93018 · doi:10.1016/S0005-1098(97)00198-2 |
| [2] | E.W. Bai, A blind approach to the Hammerstein-Wiener model identification. Automatica 38(6), 967-979 (2002) · Zbl 1012.93018 · doi:10.1016/S0005-1098(01)00292-8 |
| [3] | H.B. Chen, F. Ding, Hierarchical least squares identification for Hammerstein nonlinear controlled autoregressive systems. Circuits Syst. Signal Process. 34(1), 61-75 (2015) · Zbl 1341.93089 · doi:10.1007/s00034-014-9839-9 |
| [4] | Y.N. Cao, Z.Q. Liu, Signal frequency and parameter estimation for power systems using the hierarchical dentification principle. Math. Comput. Model. 51(5-6), 854-861 (2010) · Zbl 1202.94116 · doi:10.1016/j.mcm.2010.05.015 |
| [5] | X. Cao, D.Q. Zhu, S.X. Yang, Multi-AUV target search based on bioinspired neurodynamics model in 3-D underwater environments. IEEE Trans. Neural Netw. Learn. Syst. (2016). doi:10.1109/TNNLS.2015.2482501 |
| [6] | H.B. Chen, Y.S. Xiao, F. Ding, Hierarchical gradient parameter estimation algorithm for Hammerstein nonlinear systems using the key term separation principle. Appl. Math. Comput. 247, 1202-1210 (2014) · Zbl 1343.62055 |
| [7] | Z.Z. Chu, D.Q. Zhu, S.X. Yang, Observer-based adaptive neural network trajectory tracking control for remotely operated Vehicle. IEEE Trans. Neural Netw. Learn. Syst. (2016). doi:10.1109/TNNLS.2016.2544786 |
| [8] | F. Ding, K.P. Deng, X.M. Liu, Decomposition based Newton iterative identification method for a Hammerstein nonlinear FIR system with ARMA noise. Circuits Syst. Signal Process. 33(9), 2881-2893 (2014) · doi:10.1007/s00034-014-9772-y |
| [9] | J. Ding, C.X. Fan, J.X. Lin, Auxiliary model based parameter estimation for dual-rate output error systems with colored noise. Appl. Math. Model. 37(6), 4051-4058 (2013) · doi:10.1016/j.apm.2012.09.016 |
| [10] | J. Ding, J.X. Lin, Modified subspace identification for periodically non-uniformly sampled systems by using the lifting technique. Circuits Syst. Signal Process. 33(5), 1439-1449 (2014) · doi:10.1007/s00034-013-9704-2 |
| [11] | F. Ding, X.M. Liu, Y. Gu, An auxiliary model based least squares algorithm for a dual-rate state space system with time-delay using the data filtering. J. Franklin Inst. 353(2), 398-408 (2016) · Zbl 1395.93530 · doi:10.1016/j.jfranklin.2015.10.025 |
| [12] | F. Ding, X.H. Wang, Q.J. Chen, Y.S. Xiao, Recursive least squares parameter estimation for a class of output nonlinear systems based on the model decomposition. Circuits Syst. Signal Process. (2016). doi:10.1007/s00034-015-0190-6 · Zbl 1345.93169 |
| [13] | V.Z. Filipovic, Consistency of the robust recursive Hammerstein model identification algorithm. J. Franklin Inst. 352(5), 1932-1945 (2015) · Zbl 1395.93169 · doi:10.1016/j.jfranklin.2015.02.005 |
| [14] | L. Fang, J.D. Wang, Q.H. Zhang, Identification of extended Hammerstein systems with hysteresis-type input nonlinearities described by Preisach model. Nonlinear Dyn. 79(2), 1257-1273 (2015) · Zbl 1345.93046 · doi:10.1007/s11071-014-1740-3 |
| [15] | F. Giri, E.W. Bai, Block-oriented Nonlinear System Identification, Lecture Notes in Control and Information Sciences, vol. 404 (Springer-Verlag, Berlin, 2010) · Zbl 1201.93004 |
| [16] | S. Gibson, B. Ninness, Robust maximum-likelihood estimation of multivariable dynamic systems. Automatica 41(10), 1667-1682 (2005) · Zbl 1087.93054 · doi:10.1016/j.automatica.2005.05.008 |
| [17] | Y.B. Hu, B.L. Liu, Q. Zhou, C. Yang, Recursive extended least squares parameter estimation for Wiener nonlinear systems with moving average noises. Circuits Syst. Signal Process. 33(2), 655-664 (2014) · doi:10.1007/s00034-013-9652-x |
| [18] | Y. Ji, X.M. Liu, F. Ding, New criteria for the robust impulsive synchronization of uncertain chaotic delayed nonlinear systems. Nonlinear Dyn. 79(1), 1-9 (2015) · Zbl 1331.34108 · doi:10.1007/s11071-014-1640-6 |
| [19] | Y. Ji, X.M. Liu, Unified synchronization criteria for hybrid switching-impulsive dynamical networks. Circuits Syst. Signal Process. 34(5), 1499-1517 (2015) · Zbl 1341.93003 · doi:10.1007/s00034-014-9916-0 |
| [20] | H. Khodadadi, H. Jazayeri-Rad, Applying a dual extended Kalman filter for the nonlinear state and parameter estimations of a continuous stirred tank reactor. Comput. Chem. Eng. 35(11), 2426-2436 (2011) · doi:10.1016/j.compchemeng.2010.12.010 |
| [21] | H. Karimi, K.B. McAuley, A maximum-likelihood method for estimating parameters, stochastic disturbance intensities and measurement noise variances in nonlinear dynamic models with process disturbances. Comput. Chem. Eng. 67, 178-198 (2014) · doi:10.1016/j.compchemeng.2014.04.007 |
| [22] | J.H. Li, Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration. Appl. Math. Lett. 26(1), 91-96 (2013) · Zbl 1255.65119 · doi:10.1016/j.aml.2012.03.038 |
| [23] | X.G. Liu, J. Lu, Least squares based iterative identification for a class of multirate systems. Automatica 46(3), 549-554 (2010) · Zbl 1194.93079 · doi:10.1016/j.automatica.2010.01.007 |
| [24] | S. Mousazadeh, M. Karimi, Estimating multivariate ARCH parameters by two-stage least-squares method. Signal Process. 89(5), 921-932 (2009) · Zbl 1161.94350 · doi:10.1016/j.sigpro.2008.11.012 |
| [25] | M. Matinfar, M. Saeidy, B. Gharahsuflu, M. Eslami, Solutions of nonlinear chemistry problems by homotopy analysis. Comput. Math. Model. 25(1), 103-114 (2014) · Zbl 1305.65179 · doi:10.1007/s10598-013-9211-0 |
| [26] | J. Prakash, B. Huang, S.L. Shah, Recursive constrained state estimation using modified extended Kalman filter. Comput. Chem. Eng. 65, 9-17 (2014) · doi:10.1016/j.compchemeng.2014.02.013 |
| [27] | J. Paduart, L. Lauwers, R. Pintelon, J. Schoukens, Identification of a Wiener-Hammerstein system using the polynomial nonlinear state space approach. Control Eng. Pract. 20(11), 1133-1139 (2012) · doi:10.1016/j.conengprac.2012.06.006 |
| [28] | A. Savran, Discrete state space modeling and control of nonlinear unknown systems. ISA Trans. 52(6), 795-806 (2013) · doi:10.1016/j.isatra.2013.07.005 |
| [29] | Y. Shi, H. Fang, Kalman filter based identification for systems with randomly missing measurements in a network environment. Int. J. Control 83(3), 538-551 (2010) · Zbl 1222.93228 · doi:10.1080/00207170903273987 |
| [30] | T. Söderström, M. Hong, J. Schoukens, R. Pintelon, Accuracy analysis of time domain maximum likelihood method and sample maximum likelihood method for errors-in-variables and output error identification. Automatica 46(4), 721-727 (2010) · Zbl 1193.93180 · doi:10.1016/j.automatica.2010.01.026 |
| [31] | J. Vörös, Modeling and parameter identification of systems with multi-segment piecewise-linear characteristics. IEEE Trans. Automat. Control 47(1), 184-188 (2002) · Zbl 1364.93173 · doi:10.1109/9.981742 |
| [32] | J. Vörös, Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones. IEEE Trans. Automat. Control 48(12), 2203-2206 (2003) · Zbl 1364.93172 · doi:10.1109/TAC.2003.820146 |
| [33] | L. Vanbeylen, R. Pintelon, J. Schoukens, Blind maximum likelihood identification of Hammerstein systems. Automatica 44(12), 3139-3146 (2008) · Zbl 1153.93522 · doi:10.1016/j.automatica.2008.05.013 |
| [34] | D.Q. Wang, Least squares-based recursive and iterative estimation for output error moving average systems using data filtering. IET Control Theory Appl. 5(14), 1648-1657 (2011) · doi:10.1049/iet-cta.2010.0416 |
| [35] | D.Q. Wang, Hierarchical parameter estimation for a class of MIMO Hammerstein systems based on the reframed models. Appl. Math. Lett. 57, 13-19 (2016) · Zbl 1336.93155 · doi:10.1016/j.aml.2015.12.018 |
| [36] | D.W. Wang, F. Ding, Parameter estimation algorithms for multivariable Hammerstein CARMA systems. Inf. Sci. 355, 237-248 (2016) · Zbl 1458.93130 · doi:10.1016/j.ins.2016.03.037 |
| [37] | Y.J. Wang, F. Ding, Novel data filtering based parameter identification for multiple-input multiple-output systems using the auxiliary model. Automatica (2016). doi:10.1016/j.automatica.2016.05.024 · Zbl 1343.93087 |
| [38] | Y.J. Wang, F. Ding, Recursive parameter estimation algorithms and convergence for a class of nonlinear systems with colored noise. Circuits Syst. Signal Process. (2016). doi:10.1007/s00034-015-0210-6 · Zbl 1346.93369 |
| [39] | Y.J. Wang, F. Ding, Recursive least squares algorithm and gradient algorithm for Hammerstein-Wiener systems using the data filtering. Nonlinear Dyn. 84(2), 1045-1053 (2016) · Zbl 1354.93158 · doi:10.1007/s11071-015-2548-5 |
| [40] | Y.J. Wang, F. Ding, Iterative estimation for a nonlinear IIR filter with moving average noise by means of the data filtering technique. IMA J. Math. Control Inf. (2016). doi:10.1093/imamci/dnv067 · Zbl 1417.93316 |
| [41] | Y.J. Wang, F. Ding, The filtering based iterative identification for multivariable systems. IET Control Theory Appl. 10(8), 894-902 (2016) |
| [42] | Y.J. Wang, F. Ding, The auxiliary model based hierarchical gradient algorithms and convergence analysis using the filtering technique. Signal Process. 128, 212-221 (2016) · doi:10.1016/j.sigpro.2016.03.027 |
| [43] | X.H. Wang, F. Ding, Convergence of the recursive identification algorithms for multivariate pseudo-linear regressive systems. Int. J. Adapt. Control Signal Process. (2016). doi:10.1002/acs.2642 · doi:10.1002/acs.2642 |
| [44] | C. Wang, T. Tang, Several gradient-based iterative estimation algorithms for a class of nonlinear systems using the filtering technique. Nonlinear Dynam. 77(3), 769-780 (2014) · Zbl 1314.93013 · doi:10.1007/s11071-014-1338-9 |
| [45] | J. Wang, Q. Zhang, Detection of asymmetric control valve stiction from oscillatory data using an extended Hammerstein system identification method. J. Process Control 24(1), 1-12 (2014) · doi:10.1016/j.jprocont.2013.10.012 |
| [46] | D.Q. Wang, W. Zhang, Improved least squares identification algorithm for multivariable Hammerstein systems. J. Franklin Inst. 352(11), 5292-5370 (2015) · Zbl 1395.93287 · doi:10.1016/j.jfranklin.2015.09.007 |
| [47] | W.G. Zhang, Decomposition based least squares iterative estimation for output error moving average systems. Eng. Comput. 31(4), 709-725 (2014) · doi:10.1108/EC-07-2012-0154 |
| [48] | H. Zhang, Y. Shi, A.S. Mehr, Robust H-infty PID control for multivariable networked control systems with disturbance/noise attenuation. Int. J. Robust Nonlinear Control 22(2), 183-204 (2012) · Zbl 1244.93047 · doi:10.1002/rnc.1688 |
| [49] | Z.G. Zhao, B. Huang, F. Liu, Parameter estimation in batch process using EM algorithm with particle filter. Comput. Chem. Eng. 57, 159-172 (2013) · doi:10.1016/j.compchemeng.2013.03.024 |
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