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access icon free Identification of partially known non-linear stochastic spatio-temporal dynamical systems by using a novel partially linear Kernel method

  • Author(s): Hanwen Ning 1  and  Xingjian Jing 2, 3
    • View affiliations
    • Affiliations: 1: School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, Hubei, People's Republic of China;
      2: Department of Mechanical Engineering, Hong Kong Polytechnic University, HungHom, Kowloon, Hong Kong, People's Republic of China;
      3: Hong Kong Polytechnic University, Shenzhen Research Institute, Shenzhen, People's Republic of China
  • Source: Volume 9, Issue 1, 02 January 2015, p. 21 – 33
    DOI:  10.1049/iet-cta.2014.0242 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 07/03/2014, Accepted 08/08/2014, Revised 08/07/2014, Published 24/09/2014

The identification of non-linear stochastic spatio-temporal dynamical systems given by stochastic partial differential equations is of great significance to engineering practice, since it can always provide useful insight into the mechanism and physical characteristics of the underlying dynamics. In this study, based on the difference method for stochastic partial differential equations, a novel state-space model named multi-input–multi-output extended partially linear model for stochastic spatio-temporal dynamical system is proposed. A new Reproducing Kernel Hilbert Space-based algorithm named extended partially linear least square ridge regression is thus particularly developed for the identification of the extended partially linear model. Compared with existing identification methods available for spatio-temporal dynamics, the advantages of the proposed identification method include that (i) it can make full use of the partially linear structural information of physical models, (ii) it can achieve more accurate estimation results for system non-linear dynamics and (iii) the resulting estimated model parameters have clear physical meaning or properties closely related to the underlying dynamical system. Moreover, the proposed extended partially linear model also provide a convenient state-space model for system analysis and design (e.g. controller or filter design) of the class of non-linear stochastic partial differential dynamical systems.

Inspec keywords: Hilbert spaces; spatiotemporal phenomena; nonlinear estimation; MIMO systems; regression analysis; nonlinear dynamical systems; stochastic systems; control system synthesis; partial differential equations; least mean squares methods; state-space methods

Other keywords: nonlinear system analysis; partially linear kernel method; state-space model; stochastic partial differential equations; nonlinear stochastic spatiotemporal dynamical system identification; model parameter estimation; partially linear structural information; extended partially linear least square ridge regression model; physical model; nonlinear system design; identification method; nonlinear stochastic partial differential dynamical system; multiple input multiple output extended partially linear model; kernel Hilbert space-based algorithm

Subjects: Differential equations (numerical analysis); Interpolation and function approximation (numerical analysis); Nonlinear control systems; Control system analysis and synthesis methods; Simulation, modelling and identification; Multivariable control systems; Time-varying control systems; Other topics in statistics

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