Circuits, Systems, and Signal Processing

, Volume 39, Issue 1, pp 199–222 | Cite as

Joint Parameter and Time-Delay Identification Algorithm and Its Convergence Analysis for Wiener Time-Delay Systems

  • Asma AtitallahEmail author
  • Saïda Bedoui
  • Kamel Abderrahim


New developments for parameter and time-delay identification are presented for discrete nonlinear systems with delayed input. The proposed approach is based on overparametrization approach which involves subsuming the delay term into an extended numerator polynomial of the linear block of Wiener time-delay system. On this basis, the parameter identification problem can be then solved using recursive least squares-based optimization techniques and then, the delay is calculated directly based on the extended numerator polynomial identified: For a noise-free system, all extended numerator parameters are equal to zero. However in the noisy-output case, it is necessary to introduce an upper bound and the extended parameters whose values are smaller than a threshold level should be identified as zero. Then, the delay is determined as the first number of null extended parameter values. In addition, the convergence of the identified parameter vector is studied. The performances of the proposed identification algorithms are illustrated through simulation examples.


Identification Wiener systems Time-delay estimation Parameter estimations Recursive least squares method Convergence analysis 



This work was supported by the ministry of Higher Education and Scientific Research in Tunisia.


  1. 1.
    A. Atitallah, S. Bedoui, K. Abderrahim, Identification of Wiener time delay systems based on hierarchical gradient approach, in 8th Vienna International Conference on Mathematical Modelling, Vienna, Austria, vol. 48(1), pp. 403–408 (2015)Google Scholar
  2. 2.
    A. Atitallah, S. Bedoui, K. Abderrahim, An optimal two stage identification algorithm for discrete hammerstein time delay systems. IFAC-PapersOnLine 49(10), 19–24 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    A. Atitallah, S. Bedoui, K. Abderrahim, System identification: parameter and time-delay estimation for Wiener nonlinear systems with delayed input. Trans. Inst. Meas. Control 40(3), 1035–1045 (2016)CrossRefGoogle Scholar
  4. 4.
    A. Atitallah, S. Bedoui, K. Abderrahim, New results on Wiener time delay system identification, in The 15th Annual European Control Conference ECC, pp. 1637–1642 (2016)Google Scholar
  5. 5.
    A. Atitallah, S. Bedoui, K. Abderrahim, On convergence analysis of an identification algorithm for Hammerstein–Wiener systems with unknown time-delay. IFAC-Papers OnLine 50(1), 14052–14057 (2017)CrossRefGoogle Scholar
  6. 6.
    S.A. Billings, Nonlinear System Identifications: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains (Wiely, Hoboken, 2013)CrossRefGoogle Scholar
  7. 7.
    G. Bottegal, R. Castro-Garcia, J.A.K. Suykens, A two-experiment approach to Wiener system identification. Automatica 93, 282–289 (2018)MathSciNetCrossRefGoogle Scholar
  8. 8.
    I. Dassios, Optimal solutions for non-consistent singular linear systems of fractional nabla difference equations. Circuits Syst. Signal Process. 34, 1769–1797 (2015)CrossRefGoogle Scholar
  9. 9.
    E. de Klerk, Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications (Springer, Berlin, 2002)CrossRefGoogle Scholar
  10. 10.
    F. Ding, X. Liu, M. Liu, The recursive least squares identification algorithm for a class of Wiener nonlinear systems. J. Franklin Inst. 353(7), 1518–1526 (2016)MathSciNetCrossRefGoogle Scholar
  11. 11.
    C. Elisei-Iliescu, C. Paleologu, J. Benesty, C. Stanciu, C. Anghel, S. Ciochin\(\check{a}\), Recursive least-squares algorithms for the identification of low-rank systems. IEEE/ACM Trans. Audio Speech Lang. Process. 27(5), 903–918 (2019)CrossRefGoogle Scholar
  12. 12.
    R.K.H. Galvao, S. Hadjiloucas, A. Izhac, J.W. Bowen, Wiener-system subspace identification for mobile wireless mm-wave networks. IEEE Trans. Veh. Technol. 56(4), 1935–1948 (2007)CrossRefGoogle Scholar
  13. 13.
    F. Giri, E.W. Bai, Block-Oriented Nonlinear System Identification (Springer, Berlin, 2010)CrossRefGoogle Scholar
  14. 14.
    J. Guo, L.Y. Wang, G. Yin, Y. Zhao, J.F. Zhang, Identification of Wiener systems with quantized inputs and binary-valued output observations. Automatica 78, 280–286 (2017)MathSciNetCrossRefGoogle Scholar
  15. 15.
    D.A. Harville, Matrix Algebra from a Statistician’s Perspective (Springer, Berlin, 2008)zbMATHGoogle Scholar
  16. 16.
    Y. Hu, Q. Zhou, H. Yu, Z. Zhou, F. Ding, Two-stage generalized projection identification algorithms for stochastic systems. Circuits Syst. Signal Process. 38(6), 2846–2862 (2019). CrossRefGoogle Scholar
  17. 17.
    W. Huang, X. Li, S. Yang, Y. Qian, Dynamic flexibility analysis of chemical reaction systems with time delay: using a modified finite element collocation method. Chem. Eng. Res. Des. 89(10), 1938–1946 (2011)CrossRefGoogle Scholar
  18. 18.
    Y.L. Hsu, J.S. Wang, A Wiener-type recurrent neural network and its control strategy for nonlinear dynamic applications. J. Process Control 19, 942–953 (2009). CrossRefGoogle Scholar
  19. 19.
    I.W. Hunter, M.J. Korenberg, The identification of nonlinear biological systems: Wiener and Hammerstein Cascade models. Biol. Cybern. 55(2–3), 135–144 (1986)MathSciNetzbMATHGoogle Scholar
  20. 20.
    R. Kanthasamy, H. Anwaruddin, S.K. Sinnadurai, A new approach to the identification of distillation column based on Hammerstein model. Model. Simul. Eng. 2014, 1–7 (2014). CrossRefGoogle Scholar
  21. 21.
    J. Li, W.X. Zheng, J. Gu, L. Hua, A recursive identification algorithm for wiener nonlinear systems with linear state-space subsystem. Circuits Syst. Signal Process. 37(6), 2374–2393 (2018)MathSciNetCrossRefGoogle Scholar
  22. 22.
    M. Liu, I. Dassios, F. Milano, On the stability analysis of systems of neutral delay differential equations. Circuits Syst. Signal Process. 38(4), 1639–1653 (2018)MathSciNetCrossRefGoogle Scholar
  23. 23.
    W. Liu, W. Na, L. Zhu, J. Ma, Q.J. Zhang, A Wienertype dynamic neural network approach to the modeling of nonlinear microwave devices. IEEE Trans. Microw. Theory 65, 2043–2062 (2017)CrossRefGoogle Scholar
  24. 24.
    X. Luan, Q. Chen, P. Albertos, F. Liu, Conversion of SISO processes with multiple time-delays to single time-delay processes. J. Process Control 65, 84–90 (2018)CrossRefGoogle Scholar
  25. 25.
    F. Milano, I. Dassios, Small-signal stability analysis for non-index 1 Hessenberg form systems of delay differential-algebraic equations. IEEE Trans. Circuits Syst. I Regular Papers 63(9), 1521–1530 (2016)MathSciNetCrossRefGoogle Scholar
  26. 26.
    T. Müller, M. Lauk, M. Reinhard, A. Hetzel, C.H. Lücking, J. Timmer, Estimation of delay times in biological systems. Ann. Bio. Eng. 431(11), 1423–1439 (2003)CrossRefGoogle Scholar
  27. 27.
    O. Nelles, Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models, Editions (Springer, Berlin, 2001)CrossRefGoogle Scholar
  28. 28.
    S.I. Niculescu, Delay Effects on Stability: A Robust Control Approach (Springer, Berlin, 2001)zbMATHGoogle Scholar
  29. 29.
    S.J. Norquay, A. Palazoglu, J.A. Romagnoli, Application of Wiener model predictive control (WMPC) to a pH neutralization experiment. IEEE Trans. Control Syst. Technol 7(4), 437–445 (1999)CrossRefGoogle Scholar
  30. 30.
    A. O’Dwyer, Time delay estimation in signal processing applications: an overview, in IT & T Conference, October, pp. 1–6 (2002)Google Scholar
  31. 31.
    P.S. Pal, R. Kar, D. Mandal, S.P. Ghoshal, Parametric identification with performance assessment of Wiener systems using brain storm optimization algorithm. Circuits Syst. Signal Process 36(8), 3143–3181 (2017)CrossRefGoogle Scholar
  32. 32.
    C. Reutenauer, M.P. Schotzenberger, A formula for the determinant of a sum of matrices. Lett. Math. Phys. 13, 299–302 (1987)MathSciNetCrossRefGoogle Scholar
  33. 33.
    J.P. Richard, Time-delay systems: an overview of some recent advances and open problems. Automatica 39(10), 1667–1694 (2003)MathSciNetCrossRefGoogle Scholar
  34. 34.
    M. Sbarciog, R. De Keyser, S. Cristea, C. De Prada, Nonlinear predictive control of processes with variable time delay. A temperature control case study, in 17th IEEE International Conference on Control Applications, pp. 1001–1006 (2008)Google Scholar
  35. 35.
    M. Schoukens, K. Tiels, Identification of block-oriented nonlinear systems starting from linear approximations: a survey. Automatica 85, 272–292 (2017)MathSciNetCrossRefGoogle Scholar
  36. 36.
    A. Srinivasan, P. Lakshmi, Wiener model based real-time identification and control of heat exchanger process. J. Automat. Syst. Eng. 2(1) (2008)Google Scholar
  37. 37.
    X. Wang, J. Su, L. Zhang, Time-delay estimation for SISO systems using SW\(\sigma \). ISA Trans. 80, 43–53 (2018)CrossRefGoogle Scholar
  38. 38.
    L. Yu, T.S. Qiu, A.M. Song, A time delay estimation algorithm based on the weighted correntropy spectral density. Circuits Syst. Signal Process. 36(3), 1115–1128 (2017)CrossRefGoogle Scholar
  39. 39.
    L. Zhou, X. Li, F. Pan, Least-squares-based iterative identification algorithm for Wiener nonlinear systems. J. Appl. Math. 2013, 1–6 (2013). MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Asma Atitallah
    • 1
    Email author
  • Saïda Bedoui
    • 1
  • Kamel Abderrahim
    • 1
  1. 1.Research Laboratory of Numerical Control of Industrial Processes, National Engineering School of GabesUniversity of GabesGabésTunisia

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