Nonlinear Dynamics

, Volume 95, Issue 1, pp 73–86 | Cite as

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

  • Xunde DongEmail author
  • Cong Wang
  • Qigui Yang
  • Wenjie Si
Original Paper


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.


System identification System dynamics Deterministic learning Radial basis function neural network 


Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Automation Science and EngineeringSouth China University of TechnologyGuangzhouChina
  2. 2.School of MathematicaSouth China University of TechnologyGuangzhouChina

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