Internet of Things and Cloud Computing

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Identification of Nonlinear Model with General Disturbances

Received: 05 February 2018    Accepted: 25 February 2018    Published: 26 March 2018
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Abstract

The nonlinear model has a linear dynamic system following some static nonlinearity. The dominating approach to estimate the components of this model has been to minimize the error between the simulated and the measured outputs. For the special case of Gaussian input signals, we estimate the linear part of the Hammerstein model using the Bussgang’s classic theorem. For the case with general disturbances, we derive the Maximum Likelihood method. Finally one simulation example is used to prove the efficiency of our theory.

DOI 10.11648/j.iotcc.20180601.13
Published in Internet of Things and Cloud Computing (Volume 6, Issue 1, March 2018)
Page(s) 17-24
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

System Identification, Nonlinear System, Bussgang’s Theorem, Maximum Likelihood Method

References
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[3] M Vidyasagar, Rajeeva L Karandikar. “A learning theory approach to system identification and stochastic adaptive control,” Journal of Process Control, vol 18, no 3, pp. 421-430, 2008.
[4] M C Campi, P R Kumar. “Learning dynamical systems in a stationary environment,” Systems & Control Letters, vol 34, no 3, pp. 125-132, 1998.
[5] G Calafiore, M C Campi. “Uncertain convex programs: randomized solutions and confidence levels,” Mathematical Programming, vol 102, no 11, pp. 25-46, 2005.
[6] M Milanese, C Novara. “Set membership identification of nonlinear systems,” Automatica, vol 40, no 6, pp. 957-975, 2004.
[7] T Alamo, J M Bravo, E F Camacho. “Guaranteed state estimation by zonotopes,” Automatica, vol 41, no 6, pp. 1035-1043, 2005.
[8] J M Bravo, T Alamo, E F Camacho. “Bounded error identification of systems with time varying parameters,” IEEE Transaction on Automatic Control, vol 51, no 7, pp. 1144-1150, 2006.
[9] J M Bravo, A Suarez, M Vasallo. “Slide window bounded error tome varying systems identification,” IEEE Transaction on Automatic Control, vol 61, no 8, pp. 2282-2287, 2016.
[10] J M Bravo, T Alamo, M Vasallo. “A general framework for predictions based on bounding techniques and local approximation,” IEEE Transaction on Automatic Control, vol 62, no 7, pp. 3430-3435, 2017.
[11] Marko Tanaskovic, Lorenzo Fagiano, Roy Smith. “Adaptive receding horizon control for constrained MIMO systems,” Automatica, vol 50, no 12, pp. 3019-3029, 2014.
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Author Information
  • School of Mechanical and Electronic Engineering, Jingdezhen Ceramic Institute, Jingdezhen, China

  • School of Mechanical and Electronic Engineering, Jingdezhen Ceramic Institute, Jingdezhen, China

  • School of Electronic Engineering and Automation, Jiangxi University of Science and Technology, Ganzhou, China

  • School of Electronic Engineering and Automation, Jiangxi University of Science and Technology, Ganzhou, China

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  • APA Style

    Wang Xiaoping, Yao Jie, Wang Jianhong, Liu Feifei. (2018). Identification of Nonlinear Model with General Disturbances. Internet of Things and Cloud Computing, 6(1), 17-24. https://doi.org/10.11648/j.iotcc.20180601.13

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    ACS Style

    Wang Xiaoping; Yao Jie; Wang Jianhong; Liu Feifei. Identification of Nonlinear Model with General Disturbances. Internet Things Cloud Comput. 2018, 6(1), 17-24. doi: 10.11648/j.iotcc.20180601.13

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    AMA Style

    Wang Xiaoping, Yao Jie, Wang Jianhong, Liu Feifei. Identification of Nonlinear Model with General Disturbances. Internet Things Cloud Comput. 2018;6(1):17-24. doi: 10.11648/j.iotcc.20180601.13

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  • @article{10.11648/j.iotcc.20180601.13,
      author = {Wang Xiaoping and Yao Jie and Wang Jianhong and Liu Feifei},
      title = {Identification of Nonlinear Model with General Disturbances},
      journal = {Internet of Things and Cloud Computing},
      volume = {6},
      number = {1},
      pages = {17-24},
      doi = {10.11648/j.iotcc.20180601.13},
      url = {https://doi.org/10.11648/j.iotcc.20180601.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.iotcc.20180601.13},
      abstract = {The nonlinear model has a linear dynamic system following some static nonlinearity. The dominating approach to estimate the components of this model has been to minimize the error between the simulated and the measured outputs. For the special case of Gaussian input signals, we estimate the linear part of the Hammerstein model using the Bussgang’s classic theorem. For the case with general disturbances, we derive the Maximum Likelihood method. Finally one simulation example is used to prove the efficiency of our theory.},
     year = {2018}
    }
    

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  • TY  - JOUR
    T1  - Identification of Nonlinear Model with General Disturbances
    AU  - Wang Xiaoping
    AU  - Yao Jie
    AU  - Wang Jianhong
    AU  - Liu Feifei
    Y1  - 2018/03/26
    PY  - 2018
    N1  - https://doi.org/10.11648/j.iotcc.20180601.13
    DO  - 10.11648/j.iotcc.20180601.13
    T2  - Internet of Things and Cloud Computing
    JF  - Internet of Things and Cloud Computing
    JO  - Internet of Things and Cloud Computing
    SP  - 17
    EP  - 24
    PB  - Science Publishing Group
    SN  - 2376-7731
    UR  - https://doi.org/10.11648/j.iotcc.20180601.13
    AB  - The nonlinear model has a linear dynamic system following some static nonlinearity. The dominating approach to estimate the components of this model has been to minimize the error between the simulated and the measured outputs. For the special case of Gaussian input signals, we estimate the linear part of the Hammerstein model using the Bussgang’s classic theorem. For the case with general disturbances, we derive the Maximum Likelihood method. Finally one simulation example is used to prove the efficiency of our theory.
    VL  - 6
    IS  - 1
    ER  - 

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