An affine Gaussian process approach for nonlinear system identification

• Autorzy: Gregorcic G. , Lightbody G.
• Języki publikacji: EN

Abstrakty

EN

The traditional Gaussian Process model is not analytically invertible. In order to use the Gaussian Process model for Internal Model Control, numerical approaches have to be used to find the inverse of the model. The numerical search for the inverse of each sample increases the already large computational load. To reduce the computation load an Affine Local Gaussian Process Model Network, as a combination of traditional Local Model Network and non-parametrical Gaussian Process Prior approach, is proposed in this paper. A novel algorithm for structure optimisation is introduced and exact inverse of the proposed network is derived. An Affine Local Gaussian Process Model Network and its inverse are illustrated on a simulated example.

Słowa kluczowe

EN

computational methods; neural networks; fuzzy sets; probability; regression analysis; approximation theory; optimization; computer simulation

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Systems Science
• Rocznik: 2003
• Tom: Vol. 29, nr 2
• Strony: 47--63
• Opis fizyczny: Bibliogr. 18 poz.,

Twórcy

autor

Gregorcic G.

• Department of Electrical Engineering, University College Cork, Cork, Ireland

autor

Lightbody G.

• Department of Electrical Engineering, University College Cork, Cork, Ireland

Bibliografia

• [1] Narendra K. S., Parthasarathy K., Identification and control of dynamical systems using neural networks, IEEE Transactions on Neural Networks, 1(1), Mar. 1990, 4-27.
• [2] Takagi T., Sugeno M., Fuzzy identification of systems and its applications to modelling and control, IEEE Transactions on Systems, Man and Cybernetics, SMC-15(1), Jan.-Feb. 1985, 116-132.
• [3] Murray-Smith R., Johansen T. A. (eds.). Multiple Model Approaches to Modelling and Control Taylor and Francis, London 1997.
• [4] Brown M. D., Lightbody G., Irwin G. W., Nonlinear internal model control using local model networks, lEE Proceedings: Control Theory and Applications, 144(6), Nov. 1997, 505-514.
• [5] Johansen T. A., Murray-Smith R., Shorten R., On transient dynamics, off-equlibrium behaviour and identification in blended multiple model structures, European Control Conference, 1999.
• [6] O'Hagan A., Curve fitting and optimal design for prediction {with discussion). Journal of the Royal Statistical Society B, 40(1), 1978, 1-42.
• [7] Williams C. K. I., Prediction with Gaussian processes: From linear regression to linear prediction and beyond. Learning and Inference in Graphical Models, 1998.
• [8] Leith D. J., Leithead W. E., Murray-Smith R., Nonlinear structure identification: A Gaussian process/velocity-based approach, 2001.
• [9] Murray-Smith R., Sbarbaro D., Nonlinear adaptive control using nonparametric Gaussian process model. International Federation of Automatic Control, 15th IFAC Triennial World Congress, 2002.
• [10] Kocijan J., Gaussian process model based predictive control. Technical Report DP-8710, Jozef Stefan Institute, Dec. 2002.
• [11] Kocijan J., Murray-Smith R., Rasmussen C. E., Likar B., Predictive control with Gaussian process model. Proceedings of the IEEE Region 8 EUROCON 2003: computer as a tool, 352-356, IEEE, cop. Sep. 2003.
• [12] Gregorcic G., Lightbody G., Internal model control based on a Gaussian process prior model. Proceeding of the 2003 American Control Conference, 4981^986, IEEE, Jun. 2003.
• [13] Gibbs M. N., Bayesian Gaussian Processes for Regression and Classification, Ph.D. thesis. University of Cambridge, 1997.
• [14] Williams C. K. I., Rasmussen C. E., Gaussian processes for regression, [in:] M. E. Hasselmo Touretzky, M. C. Mozer (eds.). Advances in Neural Information Processing Systems 8, MIT Press, 1996,514-520.
• [15] Rasmussen C. E., Evaluation of Gaussian Processes and other Methods for Non-linear Regression, Ph.D. thesis. University of Toronto, 1996.
• [16] Murray-Smith R., Girard A., Gaussian process priors with arma noise models. Proceedings of The Irish Signals and Systems Conference, Maynooth, Jun. 2001, 147-152.
• [17] Gregorcic G., Ligthbody G., Gaussian processes for modelling of dynamic non-linear systems. Proceedings of the Irish Signals and Systems Conference, Cork, Jun. 2002, 141-147.
• [18]Gregorcic G., Local model network identification with Gaussian processes. Technical Report, Department of Electrical Engineering, University College Cork, Ireland, Dec. 2003.