Several gradient-based iterative estimation algorithms for a class of nonlinear systems using the filtering technique
Tóm tắt
This paper considers iterative identification problems for a class of nonlinear systems with colored noises, which can be described by a linear-in-parameters output error autoregressive model. A gradient-based iterative (GI) algorithm, a filtered GI algorithm, and a filtered three-stage GI algorithm are developed using the decomposition technique and filtering technique, and their computational efficiencies are analyzed and compared. The simulation results indicate that the proposed algorithms can estimate effectively the parameters of nonlinear systems.
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)
Hizir, N.B., Phan, M.Q., Betti, R., Longman, R.W.: Identification of discrete-time bilinear systems through equivalent linear models. Nonlinear Dyn. 69(4), 2065–2078 (2012)
Olson, C.C., Nichols, J.M., Virgin, L.N.: Parameter estimation for chaotic systems using a geometric approach: theory and experiment. Nonlinear Dyn. 70(1), 381–391 (2012)
Alarcin, F.: Nonlinear modelling of a fishing boat and fuzzy logic control design for electro-hydraulic fin stabilizer system. Nonlinear Dyn. 61(1–2), 29–41 (2010)
Togun, N., Baysec, S.: Nonlinear modeling and identification of a spark ignition engine torque. Mech. Syst. Signal Process. 26, 294–304 (2012)
Ding, F., Liu, X.P., Liu, G.: Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises. Signal Process. 89(10), 1883–1890 (2009)
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)
Chen, J., Ding, R.: An auxiliary-model-based stochastic gradient algorithm for dual-rate sampled-data Box–Jenkins systems. Circuits Syst. Signal Process. 32(5), 2475–2485 (2013)
Ding, F., Chen, H.B., Li, M.: Multi-innovation least squares identification methods based on the auxiliary model for MISO systems. Appl. Math. Comput. 187(2), 658–668 (2007)
Chen, J., Zhang, Y., Ding, R.F.: Gradient-based parameter estimation for input nonlinear systems with ARMA noises based on the auxiliary model. Nonlinear Dyn. 72(4), 865–871 (2013)
Ding, F., Liu, X.G., Chu, J.: Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle. IET Control Theory Appl. 7(2), 176–184 (2013)
Ding, F.: Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling. Appl. Math. Model. 37(4), 1694–1704 (2013)
Wang, D.Q., Ding, F.: Hierarchical least squares estimation algorithm for Hammerstein–Wiener systems. IEEE Signal Process. Lett. 19(12), 825–828 (2012)
Liu, Y.J., Ding, F., Shi, Y.: Least squares estimation for a class of non-uniformly sampled systems based on the hierarchical identification principle. Circuits Syst. Signal Process. 31(6), 1985–2000 (2012)
Ding, F., Liu, G., Liu, X.P.: Partially coupled stochastic gradient identification methods for non-uniformly sampled systems. IEEE Trans. Autom. Control 55(8), 1976–1981 (2010)
Ding, F.: Coupled-least-squares identification for multivariable systems. IET Control Theory Appl. 7(1), 68–79 (2013)
Ding, F., Chen, T.: Performance analysis of multi-innovation gradient type identification methods. Automatica 43(1), 1–14 (2007)
Ding, F., Liu, X.P., Liu, G.: Multi-innovation least squares identification for linear and pseudo-linear regression models. IEEE Trans. Syst. Man Cybernet. Part B: Cybernetics 40(3), 767–778 (2010)
Ding, F.: Several multi-innovation identification methods. Digit. Signal Process. 20(4), 1027–1039 (2010)
Zhang, J.B., Ding, F., Shi, Y.: Self-tuning control based on multi-innovation stochastic gradient parameter estimation. Syst. Control Lett. 58(1), 69–75 (2009)
Liu, Y.J., Yu, L., Ding, F.: Multi-innovation extended stochastic gradient algorithm and its performance analysis. Circuits Syst. Signal Process. 29(4), 649–667 (2010)
Liu, Y.J., Xiao, Y.S., Zhao, X.L.: Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model. Appl. Math. Comput. 215(4), 1477–1483 (2009)
Liu, Y.J., Sheng, J., Ding, R.F.: Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems. Comput. Math. Appl. 59(8), 2615–2627 (2010)
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)
Ding, J., Ding, F., Liu, X.P., Liu, G.: Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data. IEEE Trans. Autom. Control 56(11), 2677–2683 (2011)
Liu, Y.J., Ding, F., Shi, Y.: An efficient hierarchical identification method for general dual-rate sampled-data systems. Automatica 50(3), 962–973 (2014).
Ding, F., Liu, X.P., Liu, G.: Gradient based and least-squares based iterative identification methods for OE and OEMA systems. Digit. Signal Process. 20(3), 664–677 (2010)
Liu, Y.J., Wang, D.Q., Ding, F.: Least squares based iterative algorithms for identifying Box–Jenkins models with finite measurement data. Digit. Signal Process. 20(5), 1458–1467 (2010)
Bai, E.W., Li, K.: Convergence of the iterative algorithm for a general Hammerstein system identification. Automatica 46(11), 1891–1896 (2010)
Dehghan, M., Hajarian, M.: Iterative algorithmsx for the generalized centro-symmetric and central anti-symmetric solutions of general coupled matrix equations. Eng. Comput. 29(5), 528–560 (2012)
Dehghan, M., Hajarian, M.: Fourth-order variants of Newton’s method without second derivatives for solving non-linear equations. Eng. Comput. 29(4), 356–365 (2012)
Ding, F.: Two-stage least squares based iterative estimation algorithm for CARARMA system modeling. Appl. Math. Model. 37(7), 4798–4808 (2013)
Ding, F., Ma, J.X., Xiao, Y.S.: Newton iterative identification for a class of output nonlinear systems with moving average noises. Nonlinear Dyn. 74(1–2), 21–30 (2013)
Li, J.H., Ding, F., Hua, L.: Maximum likelihood Newton recursive and the Newton iterative estimation algorithms for Hammerstein CARAR systems. Nonlinear Dyn. 75(1–2), 235–245 (2014)
Shen, Q.Y., Ding, F.: Iterative estimation methods for Hammerstein controlled autoregressive moving average systems based on the key-term separation principle. Nonlinear Dyn. 75(4), 709–716 (2014)
Wang, D.Q., Ding, F.: Least squares based and gradient based iterative identification for Wiener nonlinear systems. Signal Process. 91(5), 1182–1189 (2011)
Liu, Y., Bai, E.W.: Iterative identification of Hammerstein systems. Automatica 43(2), 346–354 (2007)
Wang, D.Q., Ding, F., Liu, X.M.: Least squares algorithm for an input nonlinear system with a dynamic subspace state space model. Nonlinear Dyn. 75(1–2), 49–61 (2014)
Hu, P.P., Ding, F.: Multistage least squares based iterative estimation for feedback nonlinear systems with moving average noises using the hierarchical identification principle. Nonlinear Dyn. 73(1–2), 583–592 (2013)
Ding, F.: Decomposition based fast least squares algorithm for output error systems. Signal Process. 93(5), 1235–1242 (2013)
Ding, F., Duan, H.H.: Two-stage parameter estimation algorithms for Box–Jenkins systems. IET Control Theory Appl. 7(8), 646–654 (2013)
Wang, D.Q., Ding, F.: Input–output data filtering based recursive least squares parameter estimation for CARARMA systems. Digit. Signal Process. 20(4), 991–999 (2010)
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)
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)
Wang, D.Q., Shan, T., Ding, R.: Data filtering based stochastic gradient algorithms for multivariable CARAR-like systems. Math. Model. Anal. 18(3), 374–385 (2013)
Wang, Z.Y., Shen, Y.X., Ji, Z.C., Ding, R.: Filtering based recursive least squares algorithm for Hammerstein FIR-MA systems. Nonlinear Dyn. 73(1–2), 1045–1054 (2013)
Wang, D.Q., Ding, F., Chu, Y.Y.: Data filtering based recursive least squares algorithm for Hammerstein systems using the key-term separation principle. Inf. Sci. 222, 203–212 (2013)
Wang, W., Tang, T.: Recursive least squares estimation algorithm applied to a class of linear-in-parameters output error moving average systems. Appl. Math. Lett. 29, 36–41 (2014)
Goodwin, G.C., Sin, K.S.: Adaptive Filtering Prediction and Control. Prentice-hall, Englewood Cliffs (1984)
Ding, F., Liu, X.M., Chen, H.B., Yao, G.Y.: Hierarchical gradient based and hierarchical least squares based iterative parameter identification for CARARMA systems. Signal Process. 97, 31–39 (2014)
Ding, F., Liu, X.P., Liu, G.: Identification methods for Hammerstein nonlinear systems. Digit. Signal Process. 21(2), 215–238 (2011)
Ding, F.: Combined state and least squares parameter estimation algorithms for dynamic systems. Appl. Math. Model. 38(1), 403–412 (2014)
Ding, F.: Hierarchical parameter estimation algorithms for multivariable systems using measurement information. Inf. Sci. (2014). http://dx.doi.org/10.1016/j.ins.2014.02.103
Ding, F., Deng, K.P., Liu, X.M.: Decomposition based Newton iterative identification method for a Hammerstein nonlinear FIR system with ARMA noise. Circ. Syst. Signal Process. 33, (2014). doi:10.1007/s00034-014-9772-y