access icon free Hammerstein system identification with quantised inputs and quantised output observations

This study focuses on a discrete-time Hammerstein system to investigate the identification with quantised inputs and quantised output observations. After the discussion of the system identifiability and by parameterising the static non-linear function, a three-step algorithm is proposed to estimate the unknown parameters for the identifiable system. The strong convergence and the mean-square convergence rate of the algorithm are established. It is shown that the asymptotic efficiency can be achieved in terms of the Cramér–Rao lower bound by selecting a suitable transformation matrix. A numerical simulation is given to demonstrate the effectiveness of the algorithm.

Inspec keywords: matrix algebra; nonlinear control systems; convergence of numerical methods; discrete time systems; parameter estimation

Other keywords: unknown parameter estimation; discrete-time Hammerstein system identification; transformation matrix; identifiable system; Cramér-Rao lower bound; quantised output; three-step algorithm; mean-square convergence rate; system identifiability; static nonlinear function parameterisation; asymptotic efficiency; quantised inputs

Subjects: Simulation, modelling and identification; Linear algebra (numerical analysis); Nonlinear control systems; Discrete control systems

References

    1. 1)
      • 10. Guo, J., Zhao, Y.: ‘Recursive projection algorithm on FIR system identification with binary-valued observations’, Automatica, 2013, 49, pp. 33963401.
    2. 2)
      • 11. Wang, J., Zhang, Q.: ‘Identification of FIR systems based on quantized output measurements: a quadratic programming-based method’, IEEE Trans. Automat. Control, 2015, 60, (5), pp. 14391444.
    3. 3)
      • 9. Godoy, B.I., Goodwin, G.C., Agüero, J.C., et al: ‘On identification of FIR systems having quantized output data’, Automatica, 2011, 47, pp. 19051915.
    4. 4)
      • 5. Shen, J., Tan, H., Wang, J., et al: ‘A novel routing protocol providing good transmission reliability in underwater sensor networks’, J. Internet Technol., 2015, 16, (1), pp. 171178.
    5. 5)
      • 4. Wang, T., Bi, W., Zhao, Y., et al: ‘Radar target recognition algorithm based on RCS observation sequence – set-valued identification method’, J. Syst. Sci. Complexity, 2016, 29, (3), pp. 573588.
    6. 6)
      • 14. Zhao, Y., Wang, L.Y., Yin, G., et al: ‘Identification of Hammerstein systems with quantized observations’, SIAM J. Control Optim., 2010, 48, (7), pp. 43524376.
    7. 7)
      • 18. Liu, Y., Bai, E.: ‘Iterative identification of Hammerstein systems’, Automatica, 2007, 43, (2), pp. 346354.
    8. 8)
      • 20. Guo, J., Wang, L.Y., Yin, G., et al: ‘Asymptotically efficient identification of FIR systems with quantized observations and general quantized inputs’, Automatica, 2015, 57, pp. 113122.
    9. 9)
      • 15. Zhao, W., Chen, H.F., Tempo, R., et al: ‘Recursive identification of nonparametric nonlinear systems with binary-valued output observations’. Proc. of the 54th IEEE Conf. on Decision and Control, 2015, pp. 121126.
    10. 10)
      • 16. Narendra, K., Gallman, P.: ‘An iterative method for the identification of nonlinear systems using a Hammerstein model’, IEEE Trans. Autom. Control, 1966, 11, pp. 546550.
    11. 11)
      • 13. Zhao, Y., Wang, L.Y., Yin, G., et al: ‘Identification of Wiener systems with binary-valued output observations’, Automatica, 2007, 43, pp. 17521765.
    12. 12)
      • 8. Casini, M., Garulli, A., Vicino, A.: ‘Input design in worst-case system identification with quantized measurements’, Automatica, 2012, 48, (12), pp. 29973007.
    13. 13)
      • 1. Wang, L.Y., Yin, G., Zhang, J.F., et al: ‘System identification with quantized observations’ (Birkhäuser, Boston, MA, 2010).
    14. 14)
      • 2. He, Q., Wang, L.Y., Yin, G.: ‘System identification using regular and quantized observations: applications of large deviations principles’ (Springer, New York, 2013).
    15. 15)
      • 19. Zhao, W., Chen, H.F.: ‘Recursive identification for Hammerstein system with ARX subsystem’, IEEE Trans. Autom. Control, 2007, 51, (12), pp. 19661974.
    16. 16)
      • 6. Xie, S., Wang, Y.: ‘Construction of tree network with limited delivery latency in homogeneous wireless sensor networks’, Wirel. Pers. Commun., 2014, 78, (1), pp. 231246.
    17. 17)
      • 17. Ninness, B., Gibson, S.: ‘Quantifying the accuracy of Hammerstein model estimation’, Automatica, 2002, 38, pp. 20372051.
    18. 18)
      • 12. Bottegal, G., Pillonetto, G., Hjalmarsson, H.: ‘Bayesian kernel-based system identification with quantized output data’, Statistics, 2015, 48, (28), pp. 455460.
    19. 19)
      • 7. Gustafssona, F., Karlssonb, R.: ‘Statistical results for system identification based on quantized observations’, Automatica, 2009, 45, (12), pp. 27942801.
    20. 20)
      • 3. Kang, G., Bi, W., Zhao, Y., et al: ‘A new system identification approach to identify genetic variants in sequencing studies for a binary phenotype’, Hum. Heredity, 2014, 78, (2), pp. 104116.
    21. 21)
      • 21. Wang, L.Y., Yin, G.: ‘Quantized identification with dependent noise and Fisher information ratio of communication channels’, IEEE Trans. Autom. Control, 2010, 55, (3), pp. 674690.
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