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Parameter Learning Algorithms of Hammerstein Nonlinear Systems

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Automatic Control and Emerging Technologies (ACET 2023)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 1141))

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Abstract

This paper deals with the modeling and parameter estimation of Hammerstein systems from samples of input and output data. Compared with the previous work which needs to identify the parameter vectors separately, this paper introduces a new approach for simplifying the complexity of identification algorithms. The proposed strategy is that the system model is transformed to the first order linear parameter identification model based on the Taylor expansion; and a novel least squares algorithm is proposed for estimating the coupled parameters simultaneously. Moreover, the simulation results are provided for demonstrating the performance of the proposed algorithms.

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References

  1. Xu, D., Liu, J., Yan, X., Yan, W.: A novel adaptive neural network constrained control for a multi-area interconnected power system with hybrid energy storage. IEEE Trans. Industr. Electron. 65(8), 6625–6634 (2018)

    Article  Google Scholar 

  2. Bu, X., Hou, Z.: Adaptive iterative learning control for linear systems with binary-valued observations. IEEE Trans. Neural Netw. Learn. Syst. 29(1), 232–237 (2018)

    Article  MathSciNet  Google Scholar 

  3. Ning, H., Qing, G., Tian, T., et al.: Online identification of nonlinear stochastic spatiotemporal system with multiplicative noise by robust optimal control-based kernel learning method. IEEE Trans. Neural Netw. Learn. Syst. 30(2), 389–404 (2019)

    Article  MathSciNet  Google Scholar 

  4. Zhao, Y., Fatehi, A., Huang, B.: A data-driven hybrid ARX and Markov chain modeling approach to process identification with time-varying time delays. IEEE Trans. Industr. Electron. 64(5), 4226–4236 (2017)

    Article  Google Scholar 

  5. Zhao, Y., Fatehi, A., Huang, B.: Robust estimation of ARX models with time varying time delays using variational Bayesian approach. IEEE Trans. Cybern. 48(2), 532–542 (2018)

    Article  Google Scholar 

  6. Vörös, J.: Parameter identification of discontinuous Hammerstein systems. Automatica 33(6), 1141–1146 (1997)

    Article  MathSciNet  Google Scholar 

  7. Hagenblada, A., Ljung, L., Wills, A.: Maximum likelihood identification of Wiener models. Automatica 44(11), 2697–2705 (2008)

    Article  MathSciNet  Google Scholar 

  8. Bai, E.W.: A blind approach to the Hammerstein-Wiener model identification. Automatica 38(6), 967–979 (2002)

    Article  MathSciNet  Google Scholar 

  9. Bai, E.W., Li, K.: Convergence of the iterative algorithm for a general Hammerstein system identification. Automatica 46(11), 1891–1896 (2010)

    Article  MathSciNet  Google Scholar 

  10. Ding, F., Chen, T.: Identification of Hammerstein nonlinear ARMAX systems. Automatica 41(9), 1479–1489 (2005)

    Article  MathSciNet  Google Scholar 

  11. Ding, F., Liu, X.P., Liu, G.: Identification methods for Hammerstein nonlinear systems. Digit. Signal Process. 21(2), 215–238 (2011)

    Article  Google Scholar 

  12. Chen, M.T., Ding, F., Lin, R.M., et al.: Parameter estimation for a special class of nonlinear systems by using the over-parameterisation method and the linear filter. Int. J. Syst. Sci. 50(9), 1689–1702 (2019)

    Article  MathSciNet  Google Scholar 

  13. Liu, Y., Bai, E.W.: Iterative identification of Hammerstein systems. Automatica 43(2), 346–354 (2007)

    Article  MathSciNet  Google Scholar 

  14. Chen, M.T., Lin, R.M., Ng, T.Y., Ding, F.: Particle filter-based algorithm of simultaneous output and parameter estimation for output nonlinear systems under low measurement rate constraints. Nonlinear Dyn. 107(1), 727–7741 (2022)

    Article  Google Scholar 

  15. Ma, J.X., Huang, B., Ding, F.: Iterative identification of Hammerstein parameter varying systems with parameter uncertainties based on the variational Bayesian approach. IEEE Trans. Syst. Man Cybern. Syst. 50(3), 1035–1045 (2020)

    Article  Google Scholar 

  16. Benesty, J., Paleologu, C., Ciochină, S.: On the identification of bilinear forms with the Wiener filter. IEEE Signal Process. Lett. 24(5), 653–657 (2017)

    Article  Google Scholar 

  17. Vörös, J.: Modeling and parameter identification of systems with multi-segment piecewise-linear characteristics. IEEE Trans. Autom. Control 47(1), 184–188 (2002)

    Article  Google Scholar 

  18. Ding, F., Wang, X.H.: Hierarchical stochastic gradient algorithm and its performance analysis for a class of bilinear-in-parameter systems. Circuits Syst. Signal Process. 36(4), 1393–1405 (2017)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant No. 62203187), Natural Science Foundation of Jiangsu Province (Grant No. BK20221064) and Fundamental Research Funds for the Central Universities JUSRP122049.

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Correspondence to Xiao Zhang .

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Zhang, X., Ding, F., Xu, L. (2024). Parameter Learning Algorithms of Hammerstein Nonlinear Systems. In: El Fadil, H., Zhang, W. (eds) Automatic Control and Emerging Technologies. ACET 2023. Lecture Notes in Electrical Engineering, vol 1141. Springer, Singapore. https://doi.org/10.1007/978-981-97-0126-1_33

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