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System identification of distributed parameter system with recurrent trajectory via deterministic learning and interpolation

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Abstract

In the paper, we propose a novel approach to identify distributed parameter system (DPS) with recurrent state trajectory. Different from existing literature, the system dynamics rather than parameters or structure of DPS is identified in the study. Due to the infinite-dimensional feature of DPS, the partial differential equation describing the DPS is first approximated by a set of ordinary differential equations. By employing finite difference method, the spatial derivatives at a set of spatial points are approximated. Then, the DPS dynamics at the set of spatial points is identified via deterministic learning. With the identification results, a mechanism based on interpolation method is proposed to approximate the DPS dynamics at any other spatial point. That is, we can accurately identify the DPS dynamics at any spatial point. Numerical results involving the identification of an important mathematical physics equation are presented to illustrate the validity of the approach.

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Authors and Affiliations

  1. School of Automation Science and Engineering, South China University of Technology, Guangzhou, China

    Xunde Dong, Cong Wang & Wenjie Si

  2. School of Mathematica, South China University of Technology, Guangzhou, China

    Qigui Yang

Authors
  1. Xunde Dong
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  2. Cong Wang
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  3. Qigui Yang
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  4. Wenjie Si
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Correspondence to Xunde Dong.

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The authors declare that they have no conflict of interest.

Additional information

This work was supported in part by the PhD Start-up Fund of Natural Science Foundation of Guangdong Province, China (Nos.: 2017A030310493, 2018A030310367), in part by the Fundamental Research Funds for the Central Universities (No.: 2018A030310367), in part by the National Major Scientific Instruments Development Project (No.: 61527811), in part by the Science and Technology Program of Guangzhou, China (No.: 201704020078).

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Dong, X., Wang, C., Yang, Q. et al. System identification of distributed parameter system with recurrent trajectory via deterministic learning and interpolation. Nonlinear Dyn 95, 73–86 (2019). https://doi.org/10.1007/s11071-018-4551-0

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  • DOI: https://doi.org/10.1007/s11071-018-4551-0

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