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Least-Squares Parameter Estimation Algorithm for a Class of Input Nonlinear Systems

Author

Listed:
  • Weili Xiong
  • Wei Fan
  • Rui Ding

Abstract

This paper studies least-squares parameter estimation algorithms for input nonlinear systems, including the input nonlinear controlled autoregressive (IN-CAR) model and the input nonlinear controlled autoregressive autoregressive moving average (IN-CARARMA) model. The basic idea is to obtain linear-in-parameters models by overparameterizing such nonlinear systems and to use the least-squares algorithm to estimate the unknown parameter vectors. It is proved that the parameter estimates consistently converge to their true values under the persistent excitation condition. A simulation example is provided.

Suggested Citation

  • Weili Xiong & Wei Fan & Rui Ding, 2012. "Least-Squares Parameter Estimation Algorithm for a Class of Input Nonlinear Systems," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, August.
    • Handle: RePEc:hin:jnljam:684074
    DOI: 10.1155/2012/684074
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    Cited by:

    1. Huiyi Hu & Xiao Yongsong & Rui Ding, 2013. "Multi‐Innovation Stochastic Gradient Identification Algorithm for Hammerstein Controlled Autoregressive Autoregressive Systems Based on the Key Term Separation Principle and on the Model Decomposition," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. Huamin Zhang, 2014. "Iterative Solutions of a Set of Matrix Equations by Using the Hierarchical Identification Principle," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Lincheng Zhou & Xiangli Li & Feng Pan, 2013. "Least‐Squares‐Based Iterative Identification Algorithm for Wiener Nonlinear Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. Cheng Wang & Tao Tang & Dewang Chen, 2014. "Least‐Squares Based and Gradient Based Iterative Parameter Estimation Algorithms for a Class of Linear‐in‐Parameters Multiple‐Input Single‐Output Output Error Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    5. Renzhong Feng & Yanan Zhang, 2013. "Piecewise Bivariate Hermite Interpolations for Large Sets of Scattered Data," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    6. Xue-Feng Duan & Qing-Wen Wang & Jiao-Fen Li, 2013. "On the Low‐Rank Approximation Arising in the Generalized Karhunen‐Loeve Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. Xianling Lu & Wei Zhou & Wenlin Shi, 2014. "Data Filtering Based Recursive Least Squares Algorithm for Two‐Input Single‐Output Systems with Moving Average Noises," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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