Identification of Wiener Models with Binary-Valued Output Observations

This work focuses on system identification for Wiener models, whose outputs are measured by binary sensors. It begins with the development of joint identifiability. Then, using periodic inputs, empirical distributions are used to construct identification algorithms. Convergence of the algorithms is established, and associated recursive algorithms are also developed.

[1]  E. Bai.  An optimal two stage identification algorithm for Hammerstein-Wiener nonlinear systems , 1998 .

[2]  Michel Verhaegen,et al.  Identifying MIMO Wiener systems using subspace model identification methods , 1996, Signal Process..

[3]  Le Yi Wang,et al.  System identification using binary sensors , 2003, IEEE Trans. Autom. Control..

[4]  Jacob Roll,et al.  Nonlinear system identification via direct weight optimization , 2005, Autom..

[5]  Le Yi Wang,et al.  Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm , 2022 .

[6]  P. Billingsley,et al.  Convergence of Probability Measures , 1969 .

[7]  Le Yi Wang,et al.  Identification Error Bounds and Asymptotic Distributions for Systems with Structural Uncertainties , 2006, J. Syst. Sci. Complex..

[8]  Er-Wei Bai.  Frequency domain identification of Wiener models , 2003, Autom..

[9]  Vikram Krishnamurthy.  Estimation of quantized linear errors-in-variables models , 1995, Autom..

[10]  Han-Fu Chen,et al.  Recursive identification for Wiener model with discontinuous piece-wise linear function , 2006, IEEE Transactions on Automatic Control.

[11]  D. Bernstein,et al.  Identification of FIR Wiener systems with unknown, noninvertible, polynomial nonlinearities , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[12]  Lennart Ljung,et al.  Nonlinear black-box modeling in system identification: a unified overview , 1995, Autom..

[13]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[14]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[15]  H. Kushner,et al.  Stochastic Approximation and Recursive Algorithms and Applications , 2003 .

[16]  Ian W. Hunter,et al.  Two Methods for Identifying Wiener Cascades Having Noninvertible Static Nonlinearities , 1999, Annals of Biomedical Engineering.

[17]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[18]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[19]  T. Wigren.  Approximate gradients, convergence and positive realness in recursive identification of a class of non‐linear systems , 1995 .

[20]  Le Yi Wang,et al.  Joint identification of plant rational models and noise distribution functions using binary-valued observations , 2006, Autom..

[21]  Brett Ninness,et al.  Quantifying the accuracy of Hammerstein model estimation , 2000, Autom..

[22]  M. J. Korenberg,et al.  The identification of nonlinear biological systems: Wiener and Hammerstein cascade models , 1986, Biological Cybernetics.

[23]  Jean-Marc Vesin,et al.  Stochastic gradient identification of polynomial Wiener systems: analysis and application , 2001, IEEE Trans. Signal Process..

[24]  Yves Rolain,et al.  Fast approximate identification of nonlinear systems , 2003, Autom..

[25]  Xiao-Li Hu,et al.  Strong consistence of recursive identification for Wiener systems , 2005, Autom..

[26]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[27]  José A. Romagnoli,et al.  Application of Wiener model predictive control (WMPC) to a pH neutralization experiment , 1999, IEEE Trans. Control. Syst. Technol..

[28]  T. Wigren.  Convergence analysis of recursive identification algorithms based on the nonlinear Wiener model , 1994, IEEE Trans. Autom. Control..

[29]  Torbjörn Wigren,et al.  Adaptive filtering using quantized output measurements , 1998, IEEE Trans. Signal Process..

[30]  Er-Wei Bai.  An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems , 1998, Autom..

[31]  K. Narendra,et al.  An iterative method for the identification of nonlinear systems using a Hammerstein model , 1966 .

[32]  Charles M. Grinstead,et al.  Introduction to probability , 1999, Statistics for the Behavioural Sciences.

[33]  Stephen A. Billings,et al.  Identi cation of nonlinear systems-A survey , 1980 .

[34]  Gene H. Golub,et al.  Matrix computations , 1983 .

[35]  Han-Fu Chen,et al.  Identification and Stochastic Adaptive Control , 1991 .