메뉴 건너뛰기




Volumn 37, Issue 4, 2013, Pages 1694-1704

Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling

Author keywords

Least squares; Multi innovation identification; Nonlinear system; Parameter estimation; Recursive identification; Stochastic gradient

Indexed keywords

HAMMERSTEIN SYSTEM; HIERARCHICAL IDENTIFICATION PRINCIPLE; IDENTIFICATION ALGORITHMS; LEAST SQUARE; LINEAR DYNAMICAL BLOCK; MULTI-INNOVATION IDENTIFICATION; NONLINEAR STATICS; NONLINEAR SYSTEM MODELING; RECURSIVE IDENTIFICATION; SIMULATION EXAMPLE; STOCHASTIC GRADIENT; STOCHASTIC GRADIENT ALGORITHMS;

EID: 84870248582     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2012.04.039     Document Type: Article
Times cited : (244)

References (48)
  • 1
    • 78650265249 scopus 로고    scopus 로고
    • Bias compensation methods for stochastic systems with colored noise
    • Zhang Y., Cui G.M. Bias compensation methods for stochastic systems with colored noise. Appl. Math. Model. 2011, 35(4):1709-1716.
    • (2011) Appl. Math. Model. , vol.35 , Issue.4 , pp. 1709-1716
    • Zhang, Y.1    Cui, G.M.2
  • 2
    • 81155139625 scopus 로고    scopus 로고
    • On the accuracy in errors-in-variables identification compared to prediction-error identification
    • Hjalmarsson H., Mårtensson J., Rojas C.R., Söderström T. On the accuracy in errors-in-variables identification compared to prediction-error identification. Automatica 2011, 47(12):2704-2712.
    • (2011) Automatica , vol.47 , Issue.12 , pp. 2704-2712
    • Hjalmarsson, H.1    Mårtensson, J.2    Rojas, C.R.3    Söderström, T.4
  • 3
    • 79960896426 scopus 로고    scopus 로고
    • A generalized instrumental variable estimation method for errors-in-variables identification problems
    • Söderström T. A generalized instrumental variable estimation method for errors-in-variables identification problems. Automatica 2011, 47(8):1656-1666.
    • (2011) Automatica , vol.47 , Issue.8 , pp. 1656-1666
    • Söderström, T.1
  • 4
    • 78751642037 scopus 로고    scopus 로고
    • Accuracy analysis of a covariance matching approach for identifying errors-in-variables systems
    • Söderström T., Mossberg M. Accuracy analysis of a covariance matching approach for identifying errors-in-variables systems. Automatica 2011, 47(2):272-282.
    • (2011) Automatica , vol.47 , Issue.2 , pp. 272-282
    • Söderström, T.1    Mossberg, M.2
  • 5
    • 78049235073 scopus 로고    scopus 로고
    • Unbalance estimation using linear and nonlinear regression
    • Nauclér P., Söderström T. Unbalance estimation using linear and nonlinear regression. Automatica 2010, 46(11):1752-1761.
    • (2010) Automatica , vol.46 , Issue.11 , pp. 1752-1761
    • Nauclér, P.1    Söderström, T.2
  • 6
    • 77949280626 scopus 로고    scopus 로고
    • Accuracy analysis of time domain maximum likelihood method and sample maximum likelihood method for errors-in-variables and output error identification
    • Söderström T., Hong M., Schoukens J., Pintelon R. Accuracy analysis of time domain maximum likelihood method and sample maximum likelihood method for errors-in-variables and output error identification. Automatica 2010, 46(4):721-727.
    • (2010) Automatica , vol.46 , Issue.4 , pp. 721-727
    • Söderström, T.1    Hong, M.2    Schoukens, J.3    Pintelon, R.4
  • 7
    • 78650803456 scopus 로고    scopus 로고
    • System identification of nonlinear state-space models
    • Schon T., Wills A., Ninness B. System identification of nonlinear state-space models. Automatica 2011, 47(1):39-49.
    • (2011) Automatica , vol.47 , Issue.1 , pp. 39-49
    • Schon, T.1    Wills, A.2    Ninness, B.3
  • 8
    • 79960909973 scopus 로고    scopus 로고
    • Parameterization and identification of multivariable state-space systems: a canonical approach
    • Mercère G., Bako L. Parameterization and identification of multivariable state-space systems: a canonical approach. Automatica 2011, 47(8):1547-1555.
    • (2011) Automatica , vol.47 , Issue.8 , pp. 1547-1555
    • Mercère, G.1    Bako, L.2
  • 9
    • 67349090936 scopus 로고    scopus 로고
    • Multi-innovation stochastic gradient algorithms for multi-input multi-output systems
    • Han L.L., Ding F. Multi-innovation stochastic gradient algorithms for multi-input multi-output systems. Digit. Signal Process. 2009, 19(4):545-554.
    • (2009) Digit. Signal Process. , vol.19 , Issue.4 , pp. 545-554
    • Han, L.L.1    Ding, F.2
  • 10
    • 77951141155 scopus 로고    scopus 로고
    • Kalman filter based identification for systems with randomly missing measurements in a network environment
    • Shi Y., Fang H. Kalman filter based identification for systems with randomly missing measurements in a network environment. Int. J. Contr. 2010, 83(3):538-551.
    • (2010) Int. J. Contr. , vol.83 , Issue.3 , pp. 538-551
    • Shi, Y.1    Fang, H.2
  • 11
    • 54249153250 scopus 로고    scopus 로고
    • L-2 and l-infnity filtering for multirate systems using lifted models
    • Yu B., Shi Y., Huang H. l-2 and l-infnity filtering for multirate systems using lifted models. Circuits Syst. Signal Process. 2008, 27(5):699-711.
    • (2008) Circuits Syst. Signal Process. , vol.27 , Issue.5 , pp. 699-711
    • Yu, B.1    Shi, Y.2    Huang, H.3
  • 12
    • 22344449915 scopus 로고    scopus 로고
    • Identification of Hammerstein nonlinear ARMAX systems
    • Ding F., Chen T. Identification of Hammerstein nonlinear ARMAX systems. Automatica 2005, 41(9):1479-1489.
    • (2005) Automatica , vol.41 , Issue.9 , pp. 1479-1489
    • Ding, F.1    Chen, T.2
  • 13
    • 79551472381 scopus 로고    scopus 로고
    • Identification methods for Hammerstein nonlinear systems
    • Ding F., Liu X.P., Liu G. Identification methods for Hammerstein nonlinear systems. Digit. Signal Process. 2011, 21(1):1-24.
    • (2011) Digit. Signal Process. , vol.21 , Issue.1 , pp. 1-24
    • Ding, F.1    Liu, X.P.2    Liu, G.3
  • 14
    • 79551473739 scopus 로고    scopus 로고
    • Least squares based and gradient based iterative identification for Wiener nonlinear systems
    • Wang D.Q., Ding F. Least squares based and gradient based iterative identification for Wiener nonlinear systems. Signal Process. 2011.
    • (2011) Signal Process.
    • Wang, D.Q.1    Ding, F.2
  • 15
    • 80755154802 scopus 로고    scopus 로고
    • Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems
    • Li J.H., Ding F., Yang G.W. Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems. Math. Comput. Model. 2012, 55(3-4):442-450.
    • (2012) Math. Comput. Model. , vol.55 , Issue.3-4 , pp. 442-450
    • Li, J.H.1    Ding, F.2    Yang, G.W.3
  • 16
    • 33845936054 scopus 로고    scopus 로고
    • Iterative identification of Hammerstein systems
    • Liu Y., Bai E.W. Iterative identification of Hammerstein systems. Automatica 2007, 43(2):346-354.
    • (2007) Automatica , vol.43 , Issue.2 , pp. 346-354
    • Liu, Y.1    Bai, E.W.2
  • 17
    • 33947233313 scopus 로고    scopus 로고
    • Auxiliary model based least-squares identification methods for Hammerstein output-error systems
    • Ding F., Shi Y., Chen T. Auxiliary model based least-squares identification methods for Hammerstein output-error systems. Syst. Contr. Lett. 2007, 56(5):373-380.
    • (2007) Syst. Contr. Lett. , vol.56 , Issue.5 , pp. 373-380
    • Ding, F.1    Shi, Y.2    Chen, T.3
  • 18
    • 84863012837 scopus 로고    scopus 로고
    • Gradient based least squares based iterative estimation algorithms for multi-input multi-output systems
    • Ding F., Liu Y.J., Bao B. Gradient based least squares based iterative estimation algorithms for multi-input multi-output systems. Proc. Inst. Mech. Eng. Part I: J. Syst. Control Eng. 2012, 226(1):43-55.
    • (2012) Proc. Inst. Mech. Eng. Part I: J. Syst. Control Eng. , vol.226 , Issue.1 , pp. 43-55
    • Ding, F.1    Liu, Y.J.2    Bao, B.3
  • 19
    • 77957294731 scopus 로고    scopus 로고
    • Gradient-based iterative parameter estimation for Box-Jenkins systems
    • Wang D.Q., Yang G.W., Ding R.F. Gradient-based iterative parameter estimation for Box-Jenkins systems. Comput. Math. Appl. 2010, 60(5):1200-1208.
    • (2010) Comput. Math. Appl. , vol.60 , Issue.5 , pp. 1200-1208
    • Wang, D.Q.1    Yang, G.W.2    Ding, R.F.3
  • 20
    • 77949486667 scopus 로고    scopus 로고
    • Gradient based and least-squares based iterative identification methods for OE and OEMA systems
    • Ding F., Liu X.P., Liu G. Gradient based and least-squares based iterative identification methods for OE and OEMA systems. Digit. Signal Process. 2010, 20(3):664-677.
    • (2010) Digit. Signal Process. , vol.20 , Issue.3 , pp. 664-677
    • Ding, F.1    Liu, X.P.2    Liu, G.3
  • 21
    • 84857030542 scopus 로고    scopus 로고
    • Iterative parameter identification methods for nonlinear functions
    • Li J.H., Ding R.F., Yang Y. Iterative parameter identification methods for nonlinear functions. Appl. Math. Model. 2012, 26(6):2739-2750.
    • (2012) Appl. Math. Model. , vol.26 , Issue.6 , pp. 2739-2750
    • Li, J.H.1    Ding, R.F.2    Yang, Y.3
  • 22
    • 33751236756 scopus 로고    scopus 로고
    • Performance analysis of multi-innovation gradient type identification methods
    • Ding F., Chen T. Performance analysis of multi-innovation gradient type identification methods. Automatica 2007, 43(1):1-14.
    • (2007) Automatica , vol.43 , Issue.1 , pp. 1-14
    • Ding, F.1    Chen, T.2
  • 23
    • 77954175918 scopus 로고    scopus 로고
    • Several multi-innovation identification methods
    • Ding F. Several multi-innovation identification methods. Digit. Signal Process. 2010, 20(4):1027-1039.
    • (2010) Digit. Signal Process. , vol.20 , Issue.4 , pp. 1027-1039
    • Ding, F.1
  • 24
    • 79960912040 scopus 로고    scopus 로고
    • Parameter estimation with scarce measurements
    • Ding F., Liu G., Liu X.P. Parameter estimation with scarce measurements. Automatica 2011, 47(8):1646-1655.
    • (2011) Automatica , vol.47 , Issue.8 , pp. 1646-1655
    • Ding, F.1    Liu, G.2    Liu, X.P.3
  • 25
    • 77954174920 scopus 로고    scopus 로고
    • Modeling and identification for non-uniformly periodically sampled-data systems
    • Xie L., Yang H.Z., et al. Modeling and identification for non-uniformly periodically sampled-data systems. IET Contr. Theor. Appl. 2010, 4(5):784-794.
    • (2010) IET Contr. Theor. Appl. , vol.4 , Issue.5 , pp. 784-794
    • Xie, L.1    Yang, H.Z.2
  • 26
    • 77955391352 scopus 로고    scopus 로고
    • Partially coupled stochastic gradient identification methods for non-uniformly sampled systems
    • Ding F., Liu G., Liu X.P. Partially coupled stochastic gradient identification methods for non-uniformly sampled systems. IEEE Trans. Automat. Contr. 2010, 55(8):1976-1981.
    • (2010) IEEE Trans. Automat. Contr. , vol.55 , Issue.8 , pp. 1976-1981
    • Ding, F.1    Liu, G.2    Liu, X.P.3
  • 27
    • 77950187988 scopus 로고    scopus 로고
    • Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems
    • Liu Y.J., Sheng J., Ding R.F. Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems. Comput. Math. Appl. 2010, 59(8):2615-2627.
    • (2010) Comput. Math. Appl. , vol.59 , Issue.8 , pp. 2615-2627
    • Liu, Y.J.1    Sheng, J.2    Ding, R.F.3
  • 28
    • 74149086591 scopus 로고    scopus 로고
    • Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model
    • 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. 2009, 215(4):1477-1483.
    • (2009) Appl. Math. Comput. , vol.215 , Issue.4 , pp. 1477-1483
    • Liu, Y.J.1    Xiao, Y.S.2    Zhao, X.L.3
  • 29
    • 55649109065 scopus 로고    scopus 로고
    • Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems
    • Wang D.Q., Ding F. Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems. Comput. Math. Appl. 2008, 56(12):3157-3164.
    • (2008) Comput. Math. Appl. , vol.56 , Issue.12 , pp. 3157-3164
    • Wang, D.Q.1    Ding, F.2
  • 30
    • 84869425391 scopus 로고    scopus 로고
    • Separable gradient estimation algorithm for Hammerstein systems based on decompositions
    • June 27-29, Montréal, Canada.
    • F. Ding, Separable gradient estimation algorithm for Hammerstein systems based on decompositions, in: The 2012 American Control Conference (ACC), June 27-29, 2012, Montréal, Canada.
    • (2012) The 2012 American Control Conference (ACC)
    • Ding, F.1
  • 31
    • 0032022209 scopus 로고    scopus 로고
    • An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems
    • Bai E. An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems. Automatica 1998, 34(3):333-338.
    • (1998) Automatica , vol.34 , Issue.3 , pp. 333-338
    • Bai, E.1
  • 32
    • 70349982584 scopus 로고    scopus 로고
    • Revisiting Hammerstein system identification through the two-stage algorithm for bilinear parameter estimation
    • Wang J., Zhang Q., Ljung L. Revisiting Hammerstein system identification through the two-stage algorithm for bilinear parameter estimation. Automatica 2009, 45(11):2627-2633.
    • (2009) Automatica , vol.45 , Issue.11 , pp. 2627-2633
    • Wang, J.1    Zhang, Q.2    Ljung, L.3
  • 33
    • 22144434326 scopus 로고    scopus 로고
    • Hierarchical gradient-based identification of multivariable discrete-time systems
    • Ding F., Chen T. Hierarchical gradient-based identification of multivariable discrete-time systems. Automatica 2005, 41(2):315-325.
    • (2005) Automatica , vol.41 , Issue.2 , pp. 315-325
    • Ding, F.1    Chen, T.2
  • 34
    • 16244397443 scopus 로고    scopus 로고
    • Hierarchical least squares identification methods for multivariable systems
    • Ding F., Chen T. Hierarchical least squares identification methods for multivariable systems. IEEE Trans. Automat. Contr. 2005, 50(3):397-402.
    • (2005) IEEE Trans. Automat. Contr. , vol.50 , Issue.3 , pp. 397-402
    • Ding, F.1    Chen, T.2
  • 35
    • 22144498905 scopus 로고    scopus 로고
    • Hierarchical identification of lifted state-space models for general dual-rate systems
    • Ding F., Chen T. Hierarchical identification of lifted state-space models for general dual-rate systems. IEEE Trans. Circuits Syst. - I: Regular Papers 2005, 52(6):1179-1187.
    • (2005) IEEE Trans. Circuits Syst. - I: Regular Papers , vol.52 , Issue.6 , pp. 1179-1187
    • Ding, F.1    Chen, T.2
  • 38
    • 67349177024 scopus 로고    scopus 로고
    • Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises
    • Ding F., Liu X.P., Liu G. Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises. Signal Process. 2009, 89(10):1883-1890.
    • (2009) Signal Process. , vol.89 , Issue.10 , pp. 1883-1890
    • Ding, F.1    Liu, X.P.2    Liu, G.3
  • 39
    • 16344391042 scopus 로고    scopus 로고
    • Performance bounds of the forgetting factor least squares algorithm for time-varying systems with finite measurement data
    • Ding F., Chen T. Performance bounds of the forgetting factor least squares algorithm for time-varying systems with finite measurement data. IEEE Trans. Circuites Syst. - I: Regular Papers 2005, 52(3):555-566.
    • (2005) IEEE Trans. Circuites Syst. - I: Regular Papers , vol.52 , Issue.3 , pp. 555-566
    • Ding, F.1    Chen, T.2
  • 40
    • 70350622178 scopus 로고    scopus 로고
    • An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices
    • Dehghan M., Hajarian M. An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices. Appl. Math. Model. 2010, 34(3):639-654.
    • (2010) Appl. Math. Model. , vol.34 , Issue.3 , pp. 639-654
    • Dehghan, M.1    Hajarian, M.2
  • 41
    • 79953198577 scopus 로고    scopus 로고
    • Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations
    • Dehghan M., Hajarian M. Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations. Appl. Math. Model. 2011, 35(7):3285-3300.
    • (2011) Appl. Math. Model. , vol.35 , Issue.7 , pp. 3285-3300
    • Dehghan, M.1    Hajarian, M.2
  • 42
    • 77952585183 scopus 로고    scopus 로고
    • Multi-innovation least squares identification for linear and pseudo-linear regression models
    • Ding F., X Liu P., Liu G. Multi-innovation least squares identification for linear and pseudo-linear regression models. IEEE Trans. Syst. Man Cybernet. Part B: Cybernet. 2010, 40(3):767-778.
    • (2010) IEEE Trans. Syst. Man Cybernet. Part B: Cybernet. , vol.40 , Issue.3 , pp. 767-778
    • Ding, F.1    X Liu, P.2    Liu, G.3
  • 43
    • 57249097181 scopus 로고    scopus 로고
    • Self-tuning control based on multi-innovation stochastic gradient parameter estimation
    • Zhang J.B., Ding F., Shi Y. Self-tuning control based on multi-innovation stochastic gradient parameter estimation. Syst. Contr. Lett. 2009, 58(1):69-75.
    • (2009) Syst. Contr. Lett. , vol.58 , Issue.1 , pp. 69-75
    • Zhang, J.B.1    Ding, F.2    Shi, Y.3
  • 44
    • 80455150117 scopus 로고    scopus 로고
    • Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data
    • Ding J., Ding F., Liu X.P., Liu G. Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data. IEEE Trans. Automat. Contr. 2011, 56(11):2677-2683.
    • (2011) IEEE Trans. Automat. Contr. , vol.56 , Issue.11 , pp. 2677-2683
    • Ding, J.1    Ding, F.2    Liu, X.P.3    Liu, G.4
  • 45
    • 34648843576 scopus 로고    scopus 로고
    • Adaptive fault-tolerant control of nonlinear system: an improved CMAC based fault learning approach
    • Zhu D.Q., Kong M. Adaptive fault-tolerant control of nonlinear system: an improved CMAC based fault learning approach. Int. J. Contr. 2007, 80(10):1576-1594.
    • (2007) Int. J. Contr. , vol.80 , Issue.10 , pp. 1576-1594
    • Zhu, D.Q.1    Kong, M.2
  • 46
    • 77954287475 scopus 로고    scopus 로고
    • Least squares parameter estimation with irregularly missing data
    • Ding F., Ding J. Least squares parameter estimation with irregularly missing data. Int. J. Adapt. Contr. Signal Process. 2010, 24(7):540-553.
    • (2010) Int. J. Adapt. Contr. Signal Process. , vol.24 , Issue.7 , pp. 540-553
    • Ding, F.1    Ding, J.2
  • 47
    • 58349105805 scopus 로고    scopus 로고
    • Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems
    • Ding F., Qiu L., Chen T. Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems. Automatica 2009, 45(2):324-332.
    • (2009) Automatica , vol.45 , Issue.2 , pp. 324-332
    • Ding, F.1    Qiu, L.2    Chen, T.3
  • 48
    • 46649118857 scopus 로고    scopus 로고
    • Parameter identification and intersample output estimation for dual-rate systems
    • Ding F., Liu X.P., Yang H.Z. Parameter identification and intersample output estimation for dual-rate systems. IEEE Trans. Syst. Man Cybernet. Part A: Syst. Hum. 2008, 38(4):966-975.
    • (2008) IEEE Trans. Syst. Man Cybernet. Part A: Syst. Hum. , vol.38 , Issue.4 , pp. 966-975
    • Ding, F.1    Liu, X.P.2    Yang, H.Z.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.