Data filtering-based least squares iterative algorithm for Hammerstein nonlinear systems by using the model decomposition

Springer Science and Business Media LLC - Tập 83 - Trang 1895-1908 - 2015
Junxia Ma1, Feng Ding1, Erfu Yang2
1Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi, People’s Republic of China
2Department of Design, Manufacture and Engineering Management, Space Mechatronic Systems Technology Laboratory, Strathclyde Space Institute, University of Strathclyde, Glasgow, Scotland, UK

Tóm tắt

This paper focuses on the iterative identification problems for a class of Hammerstein nonlinear systems. By decomposing the system into two fictitious subsystems, a decomposition-based least squares iterative algorithm is presented for estimating the parameter vector in each subsystem. Moreover, a data filtering-based decomposition least squares iterative algorithm is proposed. The simulation results indicate that the data filtering-based least squares iterative algorithm can generate more accurate parameter estimates than the least squares iterative algorithm.

Tài liệu tham khảo

Ding, F.: System Identification—New Theory and Methods. Science Press, Beijing (2013) Ding, F.: System Identification—Performances Analysis for Identification Methods. Science Press, Beijing (2014) KitioKwuimy, C.A., Litak, G., Nataraj, C.: Nonlinear analysis of energy harvesting systems with fractional order physical properties. Nonlinear Dyn. 80(1–2), 491–501 (2015) Huang, J., Shi, Y., Huang, H.N., Li, Z.: l-2-l-infinity filtering for multirate nonlinear sampled-data systems using T-S fuzzy models. Digit. Signal Process. 23(1), 418–426 (2013) Ji, Y., Liu, X.M., Ding, F.: New criteria for the robust impulsive synchronization of uncertain chaotic delayed nonlinear systems. Nonlinear Dyn. 79(1), 1–9 (2015) Ji, Y., Liu, X.M.: Unified synchronization criteria for hybrid switching-impulsive dynamical networks. Circuits Syst. Signal Process. 34(5), 1499–1517 (2015) Li, H., Shi, Y.: Event-triggered robust model predictive control of continuous-time nonlinear systems. Automatica 50(5), 1507–1513 (2014) Guo, Z.K., Guan, X.P.: Nonlinear generalized predictive control based on online least squares support vector machines. Nonlinear Dyn. 79(2), 1163–1168 (2015) Vörös, J.: Iterative identification of nonlinear dynamic systems with input saturation and output backlash using three-block cascade models. J. Franklin Inst. 351(12), 5455–5466 (2014) Zhang, D.L., Tang, Y.G., Ma, J.H., Guan, X.P.: Identification of wiener model with discontinuous nonlinearities using differential evolution. Int.J. Control Autom. Syst. 11(3), 511–518 (2013) Xu, L.: Application of the Newton iteration algorithm to the parameter estimation for dynamical systems. J. Comput. Appl. Math. 288, 33–43 (2015) Xu, L.: A proportional differential control method for a time-delay system using the Taylor expansion approximation. Appl. Math. Comput. 236, 391–399 (2014) Xu, L., Chen, L., Xiong, W.L.: Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration. Nonlinear Dyn. 79(3), 2155–2163 (2015) Hagenblad, A., Ljung, L., Wills, A.: Maximum likelihood identification of Wiener models. Automatica 44(11), 2697–2705 (2008) Vörös, J.: Iterative identification of nonlinear dynamic systems with output backlash using three-block cascade models. Nonlinear Dyn. 79(3), 2187–2195 (2015) Hu, Y.B., Liu, B.L., Zhou, Q., Yang, C.: Recursive extended least squares parameter estimation for Wiener nonlinear systems with moving average noises. Circuits Syst. Signal Process. 33(2), 655–664 (2014) Paduart, J., Lauwers, L., Pintelon, R., Schoukens, J.: Identification of a Wiener–Hammerstein system using the polynomial nonlinear state space approach. Control Eng. Pract. 20(11), 1133–1139 (2012) Sun, J.L., Liu, X.G.: A novel APSO-aided maximum likelihood identification method for Hammerstein systems. Nonlinear Dyn. 73(1–2), 449–462 (2013) Li, K., Peng, J.X., Bai, E.W.: A two-stage algorithm for identification of nonlinear dynamic systems. Automatica 42(7), 1189–1197 (2006) Mousazadeh, S., Karimi, M.: Estimating multivariate ARCH parameters by two-stage least-squares method. Signal Process. 89(5), 921–932 (2009) Zhang, W.G.: Decomposition based least squares iterative estimation algorithm for output error moving average systems. Eng. Comput. 31(4), 709–725 (2014) Bai, E.W., Liu, Y.: Least squares solutions of bilinear equations. Syst. Control Lett. 55(6), 466–472 (2006) Wang, D.Q., Ding, F.: Least squares based and gradient based iterative identification for Wiener nonlinear systems. Signal Process. 91(5), 1182–1189 (2011) Shi, Y., Fang, H.: Kalman filter based identification for systems with randomly missing measurements in a network environment. Int. J. Control 83(3), 538–551 (2010) Kohli, A.K., Amrita, R.: Numeric variable forgetting factor RLS algorithm for second-order Volterra filtering. Circuits Syst. Signal Process. 32(1), 223–232 (2013) Prakash, J., Huang, B., Shah, S.L.: Recursive constrained state estimation using modified extended Kalman filter. Comput. Chem. Eng. 65, 9–17 (2014) Zhao, Z.G., Huang, B., Liu, F.: Parameter estimation in batch process using EM algorithm with particle filter. Comput. Chem. Eng. 57, 159–172 (2013) Ding, F., Wang, Y.J., Ding, J.: Recursive least squares parameter identification for systems with colored noise using the filtering technique and the auxiliary model. Digit. Signal Process. 37, 100–108 (2015) Wang, C., Tang, T.: Several gradient-based iterative estimation algorithms for a class of nonlinear systems using the filtering technique. Nonlinear Dyn. 77(3), 769–780 (2014) Wang, D.Q.: 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) Ding, F., Chen, T.: Identification of Hammerstein nonlinear ARMAX systems. Automatica 41(9), 1479–1489 (2005) Li, J.H.: Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration. Appl. Math. Lett. 26(1), 91–96 (2013) Liu, Y., Bai, E.W.: Iterative identification of Hammerstein systems. Automatica 43(2), 346–354 (2007) Abrahamsson, R., Kay, S.M., Stoica, P.: Estimation of the parameters of a bilinear model with applications to submarine detection and system identification. Digit. Signal Process. 17(4), 756–773 (2007) Cao, Y.N., Liu, Z.Q.: Signal frequency and parameter estimation for power systems using the hierarchical identification principle. Math. Comput. Model. 51(5–6), 854–861 (2010) Ding, J., Fan, C.X., Lin, J.X.: Auxiliary model based parameter estimation for dual-rate output error systems with colored noise. Appl. Math. Model. 37(6), 4051–4058 (2013) Ding, J., Lin, J.X.: Modified subspace identification for periodically non-uniformly sampled systems by using the lifting technique. Circuits Syst. Signal Process. 33(5), 1439–1449 (2014) Wang, D.Q., Liu, H.B., Ding, F.: Highly efficient identification methods for dual-rate Hammerstein systems. IEEE Trans. Control Syst. Technol. 23(5), 1952–1960 (2015) Xu, L.: The damping iterative parameter identification method for dynamical systems based on the sine signal measurement. Signal Process. (2016). doi:10.1016/j.sigpro.2015.10.009 Mao, Y.W., Ding, F.: A novel data filtering based multi-innovation stochastic gradient algorithm for Hammerstein nonlinear systems. Digit. Signal Process. (2015). doi:10.1016/j.dsp.2015.07.002 Zhu, D.Q., Huang, H., Yang, S.X.: Dynamic task assignment and path planning of multi-AUV system based on an improved self-organizing map and velocity synthesis method in 3D underwater workspace. IEEE Trans. Cybernet. 43(2), 504–514 (2013) Sun, B., Zhu, D.Q., Yang, S.X.: A bio-inspired filtered backstepping cascaded tracking control of 7000m manned submarine vehicle. IEEE Trans. Ind. Electron. 61(7), 3682–3692 (2014)