Fixed-structure Gaussian process model

This article describes a method for modelling non-linear dynamic systems from measurement data. The method merges the linear local model blending approach in the velocity-based linearisation form with Bayesian Gaussian process (GP) modelling. The new Fixed-Structure GP (FSGP) model has a predetermined linear model structure with varying and probabilistic parameters represented by GP models. These models have several advantages for the modelling of local model parameters as they give us adequate results, even with small data sets. Furthermore, they provide a measure of the confidence in the prediction of the varying parameters and information about the dependence of the parameters on individual inputs. The FSGP model can be applied for the extended local linear equivalence class of non-linear systems. The obtained non-linear system model can be, for example, used for control-system design. The proposed modelling method is illustrated with a simple example of non-linear system modelling for control design.

[1]  Roderick Murray-Smith,et al.  Gaussian process priors with ARMA noise models , 2001 .

[2]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[3]  W. Leithead,et al.  Direct identification of nonlinear structure using Gaussian process prior models , 2003, 2003 European Control Conference (ECC).

[4]  Carl E. Rasmussen,et al.  Derivative Observations in Gaussian Process Models of Dynamic Systems , 2002, NIPS.

[5]  William Leithead,et al.  Global reconstruction of nonlinear systems from families of linear systems , 2002 .

[6]  J. Kocijan,et al.  An example of Gaussian process model identification , 2005 .

[7]  Robert Shorten,et al.  On the interpretation and identification of dynamic Takagi-Sugeno fuzzy models , 2000, IEEE Trans. Fuzzy Syst..

[8]  Kristjan Aû,et al.  Comprising Prior Knowledge in Dynamic Gaussian Process Models , 2005 .

[9]  T. Johansen,et al.  On transient dynamics, off-equilibrium behaviour and identification in blended multiple model structures , 1999, 1999 European Control Conference (ECC).

[10]  Igor Škrjanc,et al.  Robustness of fuzzy control and its application to a thermal plant , 2000 .

[11]  C. J. Harris,et al.  Neural Networks for Modelling and Control , 1994 .

[12]  Juš Kocijan,et al.  AN APPLICATION OF GAUSSIAN PROCESS MODELS FOR CONTROL DESIGN , 2006 .

[13]  Lennart Ljung,et al.  Regressor selection with the analysis of variance method , 2005, Autom..

[14]  Tor Arne Johansen,et al.  Non-linear predictive control using local models-applied to a batch fermentation process , 1995 .

[15]  Christopher K. I. Williams.  Prediction with Gaussian Processes: From Linear Regression to Linear Prediction and Beyond , 1999, Learning in Graphical Models.

[16]  Roderick Murray-Smith,et al.  Multiple Model Approaches to Modelling and Control , 1997 .

[17]  Agathe Girard,et al.  Dynamic systems identification with Gaussian processes , 2005 .

[18]  Yukihiro Toyoda,et al.  A parameter optimization method for radial basis function type models , 2003, IEEE Trans. Neural Networks.

[19]  Bernhard P. Lampe,et al.  Application of Laplace transformation for digital redesign of continuous control systems , 1999, IEEE Trans. Autom. Control..

[20]  W. Leithead,et al.  Analytic framework for blended multiple model systems using linear local models , 1999 .

[21]  Gordon Lightbody,et al.  Gaussian process approaches to nonlinear modelling for control , 2005 .

[22]  Gunnar Johannsen.  Knowledge-based design of human-machine interfaces , 1993 .

[23]  Stanko Strmčnik,et al.  Fuzzy gain-scheduling control of a gas-liquid separation plant implemented on a PLC , 2002 .

[24]  Niels Kjølstad Poulsen,et al.  Neural Networks for Modelling and Control of Dynamic Systems: A Practitioner’s Handbook , 2000 .

[25]  Kristian Kersting,et al.  Gaussian Process , 2010, Encyclopedia of Machine Learning.

[26]  Bojan Likar,et al.  Predictive control of a gas-liquid separation plant based on a Gaussian process model , 2007, Comput. Chem. Eng..