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Title: Identification of partially known non-linear stochastic spatio-temporal dynamical systems by using a novel partially linear Kernel method
Authors: Ning, HW
Jing, XJ 
Keywords: Nonlinear dynamical systems
Stochastic systems
Spatiotemporal phenomena
State-space methods
MIMO systems
Partial differential equations
Regression analysis
Least mean squares methods
Nonlinear estimation
Control system synthesis
Hilbert spaces
Nonlinear stochastic spatiotemporal dynamical system identification
Partially linear kernel method
Stochastic partial differential equations
State-space model
Multiple input multiple output extended partially linear model
Kernel Hilbert space-based algorithm
Extended partially linear least square ridge regression model
Identification method
Partially linear structural information
Physical model
Model parameter estimation
Nonlinear system analysis
Nonlinear system design
Nonlinear stochastic partial differential dynamical system
Issue Date: 2015
Publisher: Institution of Engineering and Technology
Source: IET control theory and applications, 2015, v. 9, no. 1, p. 21-33 How to cite?
Journal: IET control theory and applications 
Abstract: 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.
ISSN: 1751-8644 (print)
1751-8652 (online)
DOI: 10.1049/iet-cta.2014.0242
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