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

• Published in: IET control theory & applications Vol. 9; no. 1; pp. 21 - 33
• Main Authors: Ning, Hanwen, Jing, Xingjian
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 02.01.2015
• Subjects: control system synthesis; Design analysis; Design engineering; Dynamical systems; extended partially linear least square ridge regression model; Hilbert spaces; identification method; Identification methods; kernel Hilbert space‐based algorithm; least mean squares methods; MIMO systems; model parameter estimation; multiple input multiple output extended partially linear model; nonlinear dynamical systems; Nonlinear dynamics; nonlinear estimation; nonlinear stochastic partial differential dynamical system; nonlinear stochastic spatiotemporal dynamical system identification; nonlinear system analysis; nonlinear system design; Nonlinearity; Partial differential equations; partially linear kernel method; partially linear structural information; physical model; regression analysis; spatiotemporal phenomena; state‐space methods; state‐space model; stochastic partial differential equations; stochastic systems; Stochasticity; least mean squares methods; regression analysis; nonlinear estimation; nonlinear dynamical systems; identification method; kernel Hilbert space-based algorithm; model parameter estimation; stochastic systems; partially linear structural information; nonlinear system design; nonlinear stochastic spatiotemporal dynamical system identification; stochastic partial differential equations; control system synthesis; Hilbert spaces; state-space model; nonlinear stochastic partial differential dynamical system; spatiotemporal phenomena; partially linear kernel method; physical model; MIMO systems; nonlinear system analysis; partial differential equations; multiple input multiple output extended partially linear model; state-space methods; extended partially linear least square ridge regression model
• ISSN: 1751-8644; 1751-8652; 1751-8652
• DOI: 10.1049/iet-cta.2014.0242

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.