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access icon free Identification of non-linear stochastic spatiotemporal dynamical systems

  • Author(s): Hanwen Ning 1, 2 ; Xingjian Jing 1 ; Li Cheng 1
    • View affiliations
    • Affiliations: 1: Department of Mechanical Engineering, Hong Kong Polytechnic University, HungHom, Kowloon, HongKong, People's Republic of China;
      2: School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, People's Republic of China
  • Source: Volume 7, Issue 17, 21 November 2013, p. 2069 – 2083
    DOI:  10.1049/iet-cta.2013.0150 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 20/02/2013, Accepted 11/08/2013, Revised 01/08/2013, Published 21/02/2014

A systematic identification method for non-linear stochastic spatiotemproal (SST) systems described by non-linear stochastic partial differential equations (SPDEs) is investigated in this study based on pointwise observation data. A theoretical framework for a semi-finite element model approximating to an infinite-dimensional system is established, and several fundamental issues are discussed including the approximation error between the underlying infinite-dimensional dynamics and the model to be identified, and its rationality etc. Based on the proposed theoretical framework, a general identification method with irregular observation data is provided. These results not only provide an effective method for the identification of non-linear SST systems using measurement data (both offline and online), but also demonstrate a potential solution for the analysis, design and control of non-linear SST systems from a numerical point of view.

Inspec keywords: nonlinear dynamical systems; control system synthesis; stochastic systems; partial differential equations; nonlinear differential equations; identification

Other keywords: nonlinear stochastic spatio-temporal dynamical system; semifinite element model; approximation error; irregular observation data; systematic identification method; infinite-dimensional dynamic system; pointwise observation data; SPDE; general identification method; measurement data; nonlinear stochastic partial differential equations; SST systems

Subjects: Control system analysis and synthesis methods; Nonlinear control systems; Differential equations (numerical analysis); Nonlinear and functional equations (numerical analysis); Time-varying control systems; Simulation, modelling and identification

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