nips nips2002 nips2002-65 nips2002-65-reference knowledge-graph by maker-knowledge-mining
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Author: E. Solak, R. Murray-smith, W. E. Leithead, D. J. Leith, Carl E. Rasmussen
Abstract: Gaussian processes provide an approach to nonparametric modelling which allows a straightforward combination of function and derivative observations in an empirical model. This is of particular importance in identification of nonlinear dynamic systems from experimental data. 1) It allows us to combine derivative information, and associated uncertainty with normal function observations into the learning and inference process. This derivative information can be in the form of priors specified by an expert or identified from perturbation data close to equilibrium. 2) It allows a seamless fusion of multiple local linear models in a consistent manner, inferring consistent models and ensuring that integrability constraints are met. 3) It improves dramatically the computational efficiency of Gaussian process models for dynamic system identification, by summarising large quantities of near-equilibrium data by a handful of linearisations, reducing the training set size – traditionally a problem for Gaussian process models.
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[11] T. Takagi and M. Sugeno. Fuzzy identification of systems and its applications for modeling and control. IEEE Trans. on Systems, Man and Cybernetics, 15(1):116–132, 1985. Acknowledgements The authors gratefully acknowledge the support of the Multi-Agent Control Research Training Network by EC TMR grant HPRN-CT-1999-00107, support from EPSRC grant Modern statistical approaches to off-equilibrium modelling for nonlinear system control GR/M76379/01, support from EPSRC grant GR/R15863/01, and Science Foundation Ireland grant 00/PI.1/C067. Thanks to J.Q. Shi and A. Girard for useful comments. 1.5 1.5 1 1 0.5 0.5 0 0 −0.5 −0.5 −1 −1 −1.5 2 −1.5 2 2 1 2 1 1 0 1 0 0 −1 0 −1 −1 −2 u −2 −1 −2 u x (a) Derivative observations from linearisations identified from the perturbation data. 200 per linearisation ). point with noisy ( −2 x (b) Derivative observations on equilibrium, and off-equilibrium function observations from a transient trajectory. ¦ ¨ ¦ ¦ ©§ ¥ £ £¡ ¤¢ ¡ Figure 3: The manifold of equilibria on the true function. Circles indicate points at which a derivative observation is made. Crosses indicate a function observation 2.5 2 0.5 2 0.4 1.5 1.5 0.3 1 0.5 0.2 1 0 0.1 −0.5 0.5 0 −1 −0.1 −1.5 0 −0.2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 −0.5 −2 (a) Function observations −1.5 −1 −0.5 0 0.5 1 1.5 2 (b) Derivative observations −0.3 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 (c) Derivative observations £ −2.5 −2 £ Figure 4: Inferred values of function and derivatives, with contours, as and are varied along manifold of equilibria (c.f. Fig. 3) from to . Circles indicate the locations of the derivative observations points, lines indicate the uncertainty of observations ( standard deviations.) % ¥ ! ¡ ¡